Linear Algebra Lecture 35 Diagonalizable Matrices











>> YOUR LINK HERE: ___ http://youtube.com/watch?v=yEKmEtmXCU8

In this lecture, we discuss what it means for a square matrix to be diagonalizable. We prove the Diagonalization Theorem, which tells us exactly when a matrix is diagonalizable.","styleRuns":[{"startIndex":0,"length":177,"styleRunExtensions":{"styleRunColorMapExtension":{"colorMap":[{"key":"USER_INTERFACE_THEME_DARK","value":4294967295},{"key":"USER_INTERFACE_THEME_LIGHT","value":4279440147}]}},"fontFamilyName":"Roboto"}]},"headerRuns":[{"startIndex":0,"length":177,"headerMapping":"ATTRIBUTED_STRING_HEADER_MAPPING_UNSPECIFIED"}]}},{"itemSectionRenderer":{"contents":[{"continuationItemRenderer":{"trigger":"CONTINUATION_TRIGGER_ON_ITEM_SHOWN","continuationEndpoint":{"clickTrackingParams":"CM8BELsvGAIiEwj7sJvdqt6LAxUTi4wIHYclGmI=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/next"}},"continuationCommand":{"token":"Eg0SC3lFS21FdG1YQ1U4GAYyJSIRIgt5RUttRXRtWENVODAAeAJCEGNvbW1lbnRzLXNlY3Rpb24%3D","request":"CONTINUATION_REQUEST_TYPE_WATCH_NEXT"}}}}],"trackingParams":"CM8BELsvGAIiEwj7sJvdqt6LAxUTi4wIHYclGmI=","sectionIdentifier":"comment-item-section","targetId":"comments-section"}}],"trackingParams":"CM4BELovIhMI-7Cb3areiwMVE4uMCB2HJRpi"}},"secondaryResults":{"secondaryResults":{"results":[{"compactVideoRenderer":{"videoId":"p1-UN-roESM","thumbnail":{"thumbnails":[{"url":"https://i.ytimg.com/vi/p1-UN-roESM/hqdefault.jpg?sqp=-oaymwEbCKgBEF5IVfKriqkDDggBFQAAiEIYAXABwAEG rs=AOn4CLAO4DKhhb3RwrYFr84AtzYQ2WPAxw","width":168,"height":94},{"url":"https://i.ytimg.com/vi/p1-UN-roESM/hqdefault.jpg?sqp=-oaymwEcCNACELwBSFXyq4qpAw4IARUAAIhCGAFwAcABBg== rs=AOn4CLBaF2FAOn2UdrHh890y8NyrGvSAkQ","width":336,"height":188}]},"title":{"accessibility":{"accessibilityData":{"label":"Linear Algebra - Lecture 36 - Diagonalizing a Matrix by James Hamblin 31,773 views 6 years ago 9 minutes, 29 seconds"}},"simpleText":"Linear Algebra - Lecture 36 - Diagonalizing a Matrix"},"longBylineText":{"runs":[{"text":"James Hamblin","navigationEndpoint":{"clickTrackingParams":"CMgBEKQwGAAiEwj7sJvdqt6LAxUTi4wIHYclGmIyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@HamblinMath","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCNSjRxmON9JdyG-eFeNJUCQ","canonicalBaseUrl":"/@HamblinMath"}}}]},"publishedTimeText":{"simpleText":"6 years ago"},"viewCountText":{"simpleText":"31,773 views"},"lengthText":{"accessibility":{"accessibilityData":{"label":"9 minutes, 29 seconds"}},"simpleText":"9:29"},"navigationEndpoint":{"clickTrackingParams":"CMgBEKQwGAAiEwj7sJvdqt6LAxUTi4wIHYclGmIyB3JlbGF0ZWRIz5LczK3CqaHIAZoBBQgBEPgd","commandMetadata":{"webCommandMetadata":{"url":"/watch?v=p1-UN-roESM","webPageType":"WEB_PAGE_TYPE_WATCH","rootVe":3832}},"watchEndpoint":{"videoId":"p1-UN-roESM","nofollow":true,"watchEndpointSupportedOnesieConfig":{"html5PlaybackOnesieConfig":{"commonConfig":{"url":"https://rr3---sn-nv47znee.googlevideo.com/initplayback?source=youtube oeis=1 c=WEB oad=3200 ovd=3200 oaad=11000 oavd=11000 ocs=700 oewis=1 oputc=1 ofpcc=1 msp=1 odepv=1 id=a75f9437eae81123 ip=2a02%3A27aa%3A0%3A0%3A0%3A0%3A0%3Ad49 initcwndbps=1055000 mt=1740468774 oweuc="}}}}},"shortBylineText":{"runs":[{"text":"James Hamblin","navigationEndpoint":{"clickTrackingParams":"CMgBEKQwGAAiEwj7sJvdqt6LAxUTi4wIHYclGmIyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@HamblinMath","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCNSjRxmON9JdyG-eFeNJUCQ","canonicalBaseUrl":"/@HamblinMath"}}}]},"channelThumbnail":{"thumbnails":[{"url":"https://yt3.ggpht.com/ytc/AIdro_nbZ3JIBiUWnLl-e_EkqnSMgmN0nr4KLed41GbLPvWzbao=s68-c-k-c0x00ffffff-no-rj","width":68,"height":68}]},"trackingParams":"CMgBEKQwGAAiEwj7sJvdqt6LAxUTi4wIHYclGmJAo6Kg1_6G5a-nAQ==","shortViewCountText":{"accessibility":{"accessibilityData":{"label":"31K views"}},"simpleText":"31K views"},"menu":{"menuRenderer":{"items":[{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Add to queue"}]},"icon":{"iconType":"ADD_TO_QUEUE_TAIL"},"serviceEndpoint":{"clickTrackingParams":"CMwBEP6YBBgFIhMI-7Cb3areiwMVE4uMCB2HJRpi","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CMwBEP6YBBgFIhMI-7Cb3areiwMVE4uMCB2HJRpi","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"p1-UN-roESM","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CMwBEP6YBBgFIhMI-7Cb3areiwMVE4uMCB2HJRpi","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["p1-UN-roESM"],"params":"CAQ%3D"}},"videoIds":["p1-UN-roESM"]}},{"clickTrackingParams":"CMwBEP6YBBgFIhMI-7Cb3areiwMVE4uMCB2HJRpi","openPopupAction":{"popup":{"notificationActionRenderer":{"responseText":{"simpleText":"Added to queue"},"trackingParams":"CM0BELlqIhMI-7Cb3areiwMVE4uMCB2HJRpi"}},"popupType":"TOAST"}}]}},"trackingParams":"CMwBEP6YBBgFIhMI-7Cb3areiwMVE4uMCB2HJRpi"}},{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Share"}]},"icon":{"iconType":"SHARE"},"serviceEndpoint":{"clickTrackingParams":"CMgBEKQwGAAiEwj7sJvdqt6LAxUTi4wIHYclGmI=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/share/get_share_panel"}},"shareEntityServiceEndpoint":{"serializedShareEntity":"CgtwMS1VTi1yb0VTTQ%3D%3D","commands":[{"clickTrackingParams":"CMgBEKQwGAAiEwj7sJvdqt6LAxUTi4wIHYclGmI=","openPopupAction":{"popup":{"unifiedSharePanelRenderer":{"trackingParams":"CMsBEI5iIhMI-7Cb3areiwMVE4uMCB2HJRpi","showLoadingSpinner":true}},"popupType":"DIALOG","beReused":true}}]}},"trackingParams":"CMgBEKQwGAAiEwj7sJvdqt6LAxUTi4wIHYclGmI=","hasSeparator":true}}],"trackingParams":"CMgBEKQwGAAiEwj7sJvdqt6LAxUTi4wIHYclGmI=","accessibility":{"accessibilityData":{"label":"Action menu"}},"targetId":"watch-related-menu-button"}},"thumbnailOverlays":[{"thumbnailOverlayTimeStatusRenderer":{"text":{"accessibility":{"accessibilityData":{"label":"9 minutes, 29 seconds"}},"simpleText":"9:29"},"style":"DEFAULT"}},{"thumbnailOverlayToggleButtonRenderer":{"isToggled":false,"untoggledIcon":{"iconType":"WATCH_LATER"},"toggledIcon":{"iconType":"CHECK"},"untoggledTooltip":"Watch later","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CMoBEPnnAxgBIhMI-7Cb3areiwMVE4uMCB2HJRpi","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"addedVideoId":"p1-UN-roESM","action":"ACTION_ADD_VIDEO"}]}},"toggledServiceEndpoint":{"clickTrackingParams":"CMoBEPnnAxgBIhMI-7Cb3areiwMVE4uMCB2HJRpi","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"action":"ACTION_REMOVE_VIDEO_BY_VIDEO_ID","removedVideoId":"p1-UN-roESM"}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Watch later"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CMoBEPnnAxgBIhMI-7Cb3areiwMVE4uMCB2HJRpi"}},{"thumbnailOverlayToggleButtonRenderer":{"untoggledIcon":{"iconType":"ADD_TO_QUEUE_TAIL"},"toggledIcon":{"iconType":"PLAYLIST_ADD_CHECK"},"untoggledTooltip":"Add to queue","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CMkBEMfsBBgCIhMI-7Cb3areiwMVE4uMCB2HJRpi","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CMkBEMfsBBgCIhMI-7Cb3areiwMVE4uMCB2HJRpi","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"p1-UN-roESM","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CMkBEMfsBBgCIhMI-7Cb3areiwMVE4uMCB2HJRpi","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["p1-UN-roESM"],"params":"CAQ%3D"}},"videoIds":["p1-UN-roESM"]}}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Add to queue"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CMkBEMfsBBgCIhMI-7Cb3areiwMVE4uMCB2HJRpi"}},{"thumbnailOverlayNowPlayingRenderer":{"text":{"runs":[{"text":"Now playing"}]}}}],"accessibility":{"accessibilityData":{"label":"Linear Algebra - Lecture 36 - Diagonalizing a Matrix - 9 minutes, 29 seconds - Go to channel - James Hamblin - 31K views - 6 years ago - play video"}},"richThumbnail":{"movingThumbnailRenderer":{"enableHoveredLogging":true,"enableOverlay":true}}}},{"compactVideoRenderer":{"videoId":"-i4CBed-zec","thumbnail":{"thumbnails":[{"url":"https://i.ytimg.com/vi/-i4CBed-zec/hqdefault.jpg?sqp=-oaymwEbCKgBEF5IVfKriqkDDggBFQAAiEIYAXABwAEG rs=AOn4CLD6m1IYIFTh3ICJnASsNQAb48EyGA","width":168,"height":94},{"url":"https://i.ytimg.com/vi/-i4CBed-zec/hqdefault.jpg?sqp=-oaymwEcCNACELwBSFXyq4qpAw4IARUAAIhCGAFwAcABBg== rs=AOn4CLBldBVYjPtVtRmhtN3n65bUGZ-Fmw","width":336,"height":188}]},"title":{"accessibility":{"accessibilityData":{"label":"Orthogonal Diagonalization Explained | Linear Algebra by Wrath of Math 2,559 views 6 months ago 16 minutes"}},"simpleText":"Orthogonal Diagonalization Explained | Linear Algebra"},"longBylineText":{"runs":[{"text":"Wrath of Math","navigationEndpoint":{"clickTrackingParams":"CMIBEKQwGAEiEwj7sJvdqt6LAxUTi4wIHYclGmIyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@WrathofMath","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCyEKvaxi8mt9FMc62MHcliw","canonicalBaseUrl":"/@WrathofMath"}}}]},"publishedTimeText":{"simpleText":"6 months ago"},"viewCountText":{"simpleText":"2,559 views"},"lengthText":{"accessibility":{"accessibilityData":{"label":"16 minutes, 43 seconds"}},"simpleText":"16:43"},"navigationEndpoint":{"clickTrackingParams":"CMIBEKQwGAEiEwj7sJvdqt6LAxUTi4wIHYclGmIyB3JlbGF0ZWRIz5LczK3CqaHIAZoBBQgBEPgd","commandMetadata":{"webCommandMetadata":{"url":"/watch?v=-i4CBed-zec","webPageType":"WEB_PAGE_TYPE_WATCH","rootVe":3832}},"watchEndpoint":{"videoId":"-i4CBed-zec","nofollow":true,"watchEndpointSupportedOnesieConfig":{"html5PlaybackOnesieConfig":{"commonConfig":{"url":"https://rr3---sn-nv47zne7.googlevideo.com/initplayback?source=youtube oeis=1 c=WEB oad=3200 ovd=3200 oaad=11000 oavd=11000 ocs=700 oewis=1 oputc=1 ofpcc=1 msp=1 odepv=1 id=fa2e0205e77ecde7 ip=2a02%3A27aa%3A0%3A0%3A0%3A0%3A0%3Ad49 initcwndbps=1775000 mt=1740468774 oweuc="}}}}},"shortBylineText":{"runs":[{"text":"Wrath of Math","navigationEndpoint":{"clickTrackingParams":"CMIBEKQwGAEiEwj7sJvdqt6LAxUTi4wIHYclGmIyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@WrathofMath","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCyEKvaxi8mt9FMc62MHcliw","canonicalBaseUrl":"/@WrathofMath"}}}]},"channelThumbnail":{"thumbnails":[{"url":"https://yt3.ggpht.com/4dki5YPdT05Ls9qZwh7omAfETE1ygljg2ErZUPaqN0Hje01mCYKGv5nXvhBt5jXbb6efqTvFLA=s68-c-k-c0x00ffffff-no-rj","width":68,"height":68}]},"ownerBadges":[{"metadataBadgeRenderer":{"icon":{"iconType":"CHECK_CIRCLE_THICK"},"style":"BADGE_STYLE_TYPE_VERIFIED","tooltip":"Verified","trackingParams":"CMIBEKQwGAEiEwj7sJvdqt6LAxUTi4wIHYclGmI=","accessibilityData":{"label":"Verified"}}}],"trackingParams":"CMIBEKQwGAEiEwj7sJvdqt6LAxUTi4wIHYclGmJA55v7u97AgJf6AQ==","shortViewCountText":{"accessibility":{"accessibilityData":{"label":"2.5K views"}},"simpleText":"2.5K views"},"menu":{"menuRenderer":{"items":[{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Add to queue"}]},"icon":{"iconType":"ADD_TO_QUEUE_TAIL"},"serviceEndpoint":{"clickTrackingParams":"CMYBEP6YBBgGIhMI-7Cb3areiwMVE4uMCB2HJRpi","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CMYBEP6YBBgGIhMI-7Cb3areiwMVE4uMCB2HJRpi","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"-i4CBed-zec","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CMYBEP6YBBgGIhMI-7Cb3areiwMVE4uMCB2HJRpi","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["-i4CBed-zec"],"params":"CAQ%3D"}},"videoIds":["-i4CBed-zec"]}},{"clickTrackingParams":"CMYBEP6YBBgGIhMI-7Cb3areiwMVE4uMCB2HJRpi","openPopupAction":{"popup":{"notificationActionRenderer":{"responseText":{"simpleText":"Added to queue"},"trackingParams":"CMcBELlqIhMI-7Cb3areiwMVE4uMCB2HJRpi"}},"popupType":"TOAST"}}]}},"trackingParams":"CMYBEP6YBBgGIhMI-7Cb3areiwMVE4uMCB2HJRpi"}},{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Share"}]},"icon":{"iconType":"SHARE"},"serviceEndpoint":{"clickTrackingParams":"CMIBEKQwGAEiEwj7sJvdqt6LAxUTi4wIHYclGmI=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/share/get_share_panel"}},"shareEntityServiceEndpoint":{"serializedShareEntity":"CgstaTRDQmVkLXplYw%3D%3D","commands":[{"clickTrackingParams":"CMIBEKQwGAEiEwj7sJvdqt6LAxUTi4wIHYclGmI=","openPopupAction":{"popup":{"unifiedSharePanelRenderer":{"trackingParams":"CMUBEI5iIhMI-7Cb3areiwMVE4uMCB2HJRpi","showLoadingSpinner":true}},"popupType":"DIALOG","beReused":true}}]}},"trackingParams":"CMIBEKQwGAEiEwj7sJvdqt6LAxUTi4wIHYclGmI=","hasSeparator":true}}],"trackingParams":"CMIBEKQwGAEiEwj7sJvdqt6LAxUTi4wIHYclGmI=","accessibility":{"accessibilityData":{"label":"Action menu"}}}},"thumbnailOverlays":[{"thumbnailOverlayTimeStatusRenderer":{"text":{"accessibility":{"accessibilityData":{"label":"16 minutes, 43 seconds"}},"simpleText":"16:43"},"style":"DEFAULT"}},{"thumbnailOverlayToggleButtonRenderer":{"isToggled":false,"untoggledIcon":{"iconType":"WATCH_LATER"},"toggledIcon":{"iconType":"CHECK"},"untoggledTooltip":"Watch later","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CMQBEPnnAxgCIhMI-7Cb3areiwMVE4uMCB2HJRpi","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"addedVideoId":"-i4CBed-zec","action":"ACTION_ADD_VIDEO"}]}},"toggledServiceEndpoint":{"clickTrackingParams":"CMQBEPnnAxgCIhMI-7Cb3areiwMVE4uMCB2HJRpi","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"action":"ACTION_REMOVE_VIDEO_BY_VIDEO_ID","removedVideoId":"-i4CBed-zec"}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Watch later"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CMQBEPnnAxgCIhMI-7Cb3areiwMVE4uMCB2HJRpi"}},{"thumbnailOverlayToggleButtonRenderer":{"untoggledIcon":{"iconType":"ADD_TO_QUEUE_TAIL"},"toggledIcon":{"iconType":"PLAYLIST_ADD_CHECK"},"untoggledTooltip":"Add to queue","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CMMBEMfsBBgDIhMI-7Cb3areiwMVE4uMCB2HJRpi","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CMMBEMfsBBgDIhMI-7Cb3areiwMVE4uMCB2HJRpi","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"-i4CBed-zec","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CMMBEMfsBBgDIhMI-7Cb3areiwMVE4uMCB2HJRpi","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["-i4CBed-zec"],"params":"CAQ%3D"}},"videoIds":["-i4CBed-zec"]}}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Add to queue"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CMMBEMfsBBgDIhMI-7Cb3areiwMVE4uMCB2HJRpi"}},{"thumbnailOverlayNowPlayingRenderer":{"text":{"runs":[{"text":"Now playing"}]}}}],"accessibility":{"accessibilityData":{"label":"Orthogonal Diagonalization Explained | Linear Algebra - 16 minutes - Go to channel - Wrath of Math - 2.5K views - 6 months ago - play video"}},"richThumbnail":{"movingThumbnailRenderer":{"enableHoveredLogging":true,"enableOverlay":true}}}},{"compactVideoRenderer":{"videoId":"PFDu9oVAE-g","thumbnail":{"thumbnails":[{"url":"https://i.ytimg.com/vi/PFDu9oVAE-g/hqdefault.jpg?sqp=-oaymwEbCKgBEF5IVfKriqkDDggBFQAAiEIYAXABwAEG rs=AOn4CLD1-NoCqVbo6D5jYH3BrdtXQO1m7g","width":168,"height":94},{"url":"https://i.ytimg.com/vi/PFDu9oVAE-g/hqdefault.jpg?sqp=-oaymwEcCNACELwBSFXyq4qpAw4IARUAAIhCGAFwAcABBg== rs=AOn4CLDrj_RNyJZk3-SATcjV0k78CL65zA","width":336,"height":188}]},"title":{"accessibility":{"accessibilityData":{"label":"Eigenvectors and eigenvalues | Chapter 14, Essence of linear algebra by 3Blue1Brown 5,212,073 views 8 years ago 17 minutes"}},"simpleText":"Eigenvectors and eigenvalues | Chapter 14, Essence of linear algebra"},"longBylineText":{"runs":[{"text":"3Blue1Brown","navigationEndpoint":{"clickTrackingParams":"CLwBEKQwGAIiEwj7sJvdqt6LAxUTi4wIHYclGmIyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@3blue1brown","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCYO_jab_esuFRV4b17AJtAw","canonicalBaseUrl":"/@3blue1brown"}}}]},"publishedTimeText":{"simpleText":"8 years ago"},"viewCountText":{"simpleText":"5,212,073 views"},"lengthText":{"accessibility":{"accessibilityData":{"label":"17 minutes, 16 seconds"}},"simpleText":"17:16"},"navigationEndpoint":{"clickTrackingParams":"CLwBEKQwGAIiEwj7sJvdqt6LAxUTi4wIHYclGmIyB3JlbGF0ZWRIz5LczK3CqaHIAZoBBQgBEPgd","commandMetadata":{"webCommandMetadata":{"url":"/watch?v=PFDu9oVAE-g","webPageType":"WEB_PAGE_TYPE_WATCH","rootVe":3832}},"watchEndpoint":{"videoId":"PFDu9oVAE-g","nofollow":true,"watchEndpointSupportedOnesieConfig":{"html5PlaybackOnesieConfig":{"commonConfig":{"url":"https://rr4---sn-uxaxiv0nxx5q-nv4l.googlevideo.com/initplayback?source=youtube oeis=1 c=WEB oad=3200 ovd=3200 oaad=11000 oavd=11000 ocs=700 oewis=1 oputc=1 ofpcc=1 msp=1 odepv=1 id=3c50eef6854013e8 ip=2a02%3A27aa%3A0%3A0%3A0%3A0%3A0%3Ad49 initcwndbps=1350000 mt=1740468774 oweuc="}}}}},"shortBylineText":{"runs":[{"text":"3Blue1Brown","navigationEndpoint":{"clickTrackingParams":"CLwBEKQwGAIiEwj7sJvdqt6LAxUTi4wIHYclGmIyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@3blue1brown","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCYO_jab_esuFRV4b17AJtAw","canonicalBaseUrl":"/@3blue1brown"}}}]},"channelThumbnail":{"thumbnails":[{"url":"https://yt3.ggpht.com/ytc/AIdro_nFzZFPLxPZRHcE3SSwzdrbuWqfoWYwLAu0_2iO6blQYAU=s68-c-k-c0x00ffffff-no-rj","width":68,"height":68}]},"ownerBadges":[{"metadataBadgeRenderer":{"icon":{"iconType":"CHECK_CIRCLE_THICK"},"style":"BADGE_STYLE_TYPE_VERIFIED","tooltip":"Verified","trackingParams":"CLwBEKQwGAIiEwj7sJvdqt6LAxUTi4wIHYclGmI=","accessibilityData":{"label":"Verified"}}}],"trackingParams":"CLwBEKQwGAIiEwj7sJvdqt6LAxUTi4wIHYclGmJA6KeAqujeu6g8","shortViewCountText":{"accessibility":{"accessibilityData":{"label":"5.2 million views"}},"simpleText":"5.2M views"},"menu":{"menuRenderer":{"items":[{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Add to queue"}]},"icon":{"iconType":"ADD_TO_QUEUE_TAIL"},"serviceEndpoint":{"clickTrackingParams":"CMABEP6YBBgHIhMI-7Cb3areiwMVE4uMCB2HJRpi","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CMABEP6YBBgHIhMI-7Cb3areiwMVE4uMCB2HJRpi","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"PFDu9oVAE-g","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CMABEP6YBBgHIhMI-7Cb3areiwMVE4uMCB2HJRpi","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["PFDu9oVAE-g"],"params":"CAQ%3D"}},"videoIds":["PFDu9oVAE-g"]}},{"clickTrackingParams":"CMABEP6YBBgHIhMI-7Cb3areiwMVE4uMCB2HJRpi","openPopupAction":{"popup":{"notificationActionRenderer":{"responseText":{"simpleText":"Added to queue"},"trackingParams":"CMEBELlqIhMI-7Cb3areiwMVE4uMCB2HJRpi"}},"popupType":"TOAST"}}]}},"trackingParams":"CMABEP6YBBgHIhMI-7Cb3areiwMVE4uMCB2HJRpi"}},{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Share"}]},"icon":{"iconType":"SHARE"},"serviceEndpoint":{"clickTrackingParams":"CLwBEKQwGAIiEwj7sJvdqt6LAxUTi4wIHYclGmI=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/share/get_share_panel"}},"shareEntityServiceEndpoint":{"serializedShareEntity":"CgtQRkR1OW9WQUUtZw%3D%3D","commands":[{"clickTrackingParams":"CLwBEKQwGAIiEwj7sJvdqt6LAxUTi4wIHYclGmI=","openPopupAction":{"popup":{"unifiedSharePanelRenderer":{"trackingParams":"CL8BEI5iIhMI-7Cb3areiwMVE4uMCB2HJRpi","showLoadingSpinner":true}},"popupType":"DIALOG","beReused":true}}]}},"trackingParams":"CLwBEKQwGAIiEwj7sJvdqt6LAxUTi4wIHYclGmI=","hasSeparator":true}}],"trackingParams":"CLwBEKQwGAIiEwj7sJvdqt6LAxUTi4wIHYclGmI=","accessibility":{"accessibilityData":{"label":"Action menu"}}}},"thumbnailOverlays":[{"thumbnailOverlayTimeStatusRenderer":{"text":{"accessibility":{"accessibilityData":{"label":"17 minutes, 16 seconds"}},"simpleText":"17:16"},"style":"DEFAULT"}},{"thumbnailOverlayToggleButtonRenderer":{"isToggled":false,"untoggledIcon":{"iconType":"WATCH_LATER"},"toggledIcon":{"iconType":"CHECK"},"untoggledTooltip":"Watch later","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CL4BEPnnAxgCIhMI-7Cb3areiwMVE4uMCB2HJRpi","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"addedVideoId":"PFDu9oVAE-g","action":"ACTION_ADD_VIDEO"}]}},"toggledServiceEndpoint":{"clickTrackingParams":"CL4BEPnnAxgCIhMI-7Cb3areiwMVE4uMCB2HJRpi","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"action":"ACTION_REMOVE_VIDEO_BY_VIDEO_ID","removedVideoId":"PFDu9oVAE-g"}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Watch later"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CL4BEPnnAxgCIhMI-7Cb3areiwMVE4uMCB2HJRpi"}},{"thumbnailOverlayToggleButtonRenderer":{"untoggledIcon":{"iconType":"ADD_TO_QUEUE_TAIL"},"toggledIcon":{"iconType":"PLAYLIST_ADD_CHECK"},"untoggledTooltip":"Add to queue","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CL0BEMfsBBgDIhMI-7Cb3areiwMVE4uMCB2HJRpi","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CL0BEMfsBBgDIhMI-7Cb3areiwMVE4uMCB2HJRpi","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"PFDu9oVAE-g","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CL0BEMfsBBgDIhMI-7Cb3areiwMVE4uMCB2HJRpi","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["PFDu9oVAE-g"],"params":"CAQ%3D"}},"videoIds":["PFDu9oVAE-g"]}}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Add to queue"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CL0BEMfsBBgDIhMI-7Cb3areiwMVE4uMCB2HJRpi"}},{"thumbnailOverlayNowPlayingRenderer":{"text":{"runs":[{"text":"Now playing"}]}}}],"accessibility":{"accessibilityData":{"label":"Eigenvectors and eigenvalues | Chapter 14, Essence of linear algebra - 17 minutes - Go to channel - 3Blue1Brown - 5.2M views - 8 years ago - play video"}},"richThumbnail":{"movingThumbnailRenderer":{"movingThumbnailDetails":{"thumbnails":[{"url":"https://i.ytimg.com/an_webp/PFDu9oVAE-g/mqdefault_6s.webp?du=3000 sqp=COjn9b0G rs=AOn4CLDDJsiSvw6iC_qkPKDr6N_d9jV57g","width":320,"height":180}],"logAsMovingThumbnail":true},"enableHoveredLogging":true,"enableOverlay":true}}}},{"compactVideoRenderer":{"videoId":"0kA_VqHSpGg","thumbnail":{"thumbnails":[{"url":"https://i.ytimg.com/vi/0kA_VqHSpGg/hqdefault.jpg?sqp=-oaymwEbCKgBEF5IVfKriqkDDggBFQAAiEIYAXABwAEG rs=AOn4CLBEt6FzNGi0D7jguQEEMJBOqvDd-Q","width":168,"height":94},{"url":"https://i.ytimg.com/vi/0kA_VqHSpGg/hqdefault.jpg?sqp=-oaymwEcCNACELwBSFXyq4qpAw4IARUAAIhCGAFwAcABBg== rs=AOn4CLBOrBb_qb_TziGZ_DMjZ4oD9jKFwQ","width":336,"height":188}]},"title":{"accessibility":{"accessibilityData":{"label":"Diagonalizing 3x3 Matrix - Full Process [Passing Linear Algebra] by STEM Support 147,417 views 5 years ago 11 minutes, 57 seconds"}},"simpleText":"Diagonalizing 3x3 Matrix - Full Process [Passing Linear Algebra]"},"longBylineText":{"runs":[{"text":"STEM Support","navigationEndpoint":{"clickTrackingParams":"CLYBEKQwGAMiEwj7sJvdqt6LAxUTi4wIHYclGmIyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@stemsupport3645","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCAMTCW8gfx9TGKXxNqmQiXQ","canonicalBaseUrl":"/@stemsupport3645"}}}]},"publishedTimeText":{"simpleText":"5 years ago"},"viewCountText":{"simpleText":"147,417 views"},"lengthText":{"accessibility":{"accessibilityData":{"label":"11 minutes, 57 seconds"}},"simpleText":"11:57"},"navigationEndpoint":{"clickTrackingParams":"CLYBEKQwGAMiEwj7sJvdqt6LAxUTi4wIHYclGmIyB3JlbGF0ZWRIz5LczK3CqaHIAZoBBQgBEPgd","commandMetadata":{"webCommandMetadata":{"url":"/watch?v=0kA_VqHSpGg","webPageType":"WEB_PAGE_TYPE_WATCH","rootVe":3832}},"watchEndpoint":{"videoId":"0kA_VqHSpGg","nofollow":true,"watchEndpointSupportedOnesieConfig":{"html5PlaybackOnesieConfig":{"commonConfig":{"url":"https://rr1---sn-uxaxiv0nxx5q-nv4l.googlevideo.com/initplayback?source=youtube oeis=1 c=WEB oad=3200 ovd=3200 oaad=11000 oavd=11000 ocs=700 oewis=1 oputc=1 ofpcc=1 msp=1 odepv=1 id=d2403f56a1d2a468 ip=2a02%3A27aa%3A0%3A0%3A0%3A0%3A0%3Ad49 initcwndbps=1350000 mt=1740468774 oweuc="}}}}},"shortBylineText":{"runs":[{"text":"STEM Support","navigationEndpoint":{"clickTrackingParams":"CLYBEKQwGAMiEwj7sJvdqt6LAxUTi4wIHYclGmIyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@stemsupport3645","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCAMTCW8gfx9TGKXxNqmQiXQ","canonicalBaseUrl":"/@stemsupport3645"}}}]},"channelThumbnail":{"thumbnails":[{"url":"https://yt3.ggpht.com/ytc/AIdro_kX5EezszoIqXBfTrxQdvbS3iz28P6FOu0LES_SG70Narg=s68-c-k-c0x00ffffff-no-rj","width":68,"height":68}]},"trackingParams":"CLYBEKQwGAMiEwj7sJvdqt6LAxUTi4wIHYclGmJA6MjKjurqj6DSAQ==","shortViewCountText":{"accessibility":{"accessibilityData":{"label":"147K views"}},"simpleText":"147K views"},"menu":{"menuRenderer":{"items":[{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Add to queue"}]},"icon":{"iconType":"ADD_TO_QUEUE_TAIL"},"serviceEndpoint":{"clickTrackingParams":"CLoBEP6YBBgFIhMI-7Cb3areiwMVE4uMCB2HJRpi","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CLoBEP6YBBgFIhMI-7Cb3areiwMVE4uMCB2HJRpi","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"0kA_VqHSpGg","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CLoBEP6YBBgFIhMI-7Cb3areiwMVE4uMCB2HJRpi","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["0kA_VqHSpGg"],"params":"CAQ%3D"}},"videoIds":["0kA_VqHSpGg"]}},{"clickTrackingParams":"CLoBEP6YBBgFIhMI-7Cb3areiwMVE4uMCB2HJRpi","openPopupAction":{"popup":{"notificationActionRenderer":{"responseText":{"simpleText":"Added to queue"},"trackingParams":"CLsBELlqIhMI-7Cb3areiwMVE4uMCB2HJRpi"}},"popupType":"TOAST"}}]}},"trackingParams":"CLoBEP6YBBgFIhMI-7Cb3areiwMVE4uMCB2HJRpi"}},{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Share"}]},"icon":{"iconType":"SHARE"},"serviceEndpoint":{"clickTrackingParams":"CLYBEKQwGAMiEwj7sJvdqt6LAxUTi4wIHYclGmI=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/share/get_share_panel"}},"shareEntityServiceEndpoint":{"serializedShareEntity":"Cgswa0FfVnFIU3BHZw%3D%3D","commands":[{"clickTrackingParams":"CLYBEKQwGAMiEwj7sJvdqt6LAxUTi4wIHYclGmI=","openPopupAction":{"popup":{"unifiedSharePanelRenderer":{"trackingParams":"CLkBEI5iIhMI-7Cb3areiwMVE4uMCB2HJRpi","showLoadingSpinner":true}},"popupType":"DIALOG","beReused":true}}]}},"trackingParams":"CLYBEKQwGAMiEwj7sJvdqt6LAxUTi4wIHYclGmI=","hasSeparator":true}}],"trackingParams":"CLYBEKQwGAMiEwj7sJvdqt6LAxUTi4wIHYclGmI=","accessibility":{"accessibilityData":{"label":"Action menu"}}}},"thumbnailOverlays":[{"thumbnailOverlayTimeStatusRenderer":{"text":{"accessibility":{"accessibilityData":{"label":"11 minutes, 57 seconds"}},"simpleText":"11:57"},"style":"DEFAULT"}},{"thumbnailOverlayToggleButtonRenderer":{"isToggled":false,"untoggledIcon":{"iconType":"WATCH_LATER"},"toggledIcon":{"iconType":"CHECK"},"untoggledTooltip":"Watch later","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CLgBEPnnAxgBIhMI-7Cb3areiwMVE4uMCB2HJRpi","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"addedVideoId":"0kA_VqHSpGg","action":"ACTION_ADD_VIDEO"}]}},"toggledServiceEndpoint":{"clickTrackingParams":"CLgBEPnnAxgBIhMI-7Cb3areiwMVE4uMCB2HJRpi","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"action":"ACTION_REMOVE_VIDEO_BY_VIDEO_ID","removedVideoId":"0kA_VqHSpGg"}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Watch later"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CLgBEPnnAxgBIhMI-7Cb3areiwMVE4uMCB2HJRpi"}},{"thumbnailOverlayToggleButtonRenderer":{"untoggledIcon":{"iconType":"ADD_TO_QUEUE_TAIL"},"toggledIcon":{"iconType":"PLAYLIST_ADD_CHECK"},"untoggledTooltip":"Add to queue","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CLcBEMfsBBgCIhMI-7Cb3areiwMVE4uMCB2HJRpi","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CLcBEMfsBBgCIhMI-7Cb3areiwMVE4uMCB2HJRpi","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"0kA_VqHSpGg","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CLcBEMfsBBgCIhMI-7Cb3areiwMVE4uMCB2HJRpi","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["0kA_VqHSpGg"],"params":"CAQ%3D"}},"videoIds":["0kA_VqHSpGg"]}}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Add to queue"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CLcBEMfsBBgCIhMI-7Cb3areiwMVE4uMCB2HJRpi"}},{"thumbnailOverlayNowPlayingRenderer":{"text":{"runs":[{"text":"Now playing"}]}}}],"accessibility":{"accessibilityData":{"label":"Diagonalizing 3x3 Matrix - Full Process [Passing Linear Algebra] - 11 minutes, 57 seconds - Go to channel - STEM Support - 147K views - 5 years ago - play video"}},"richThumbnail":{"movingThumbnailRenderer":{"enableHoveredLogging":true,"enableOverlay":true}}}},{"lockupViewModel":{"contentImage":{"collectionThumbnailViewModel":{"primaryThumbnail":{"thumbnailViewModel":{"image":{"sources":[{"url":"https://i.ytimg.com/vi/HAoL5fPmgrw/hqdefault.jpg?sqp=-oaymwEWCKgBEF5IWvKriqkDCQgBFQAAiEIYAQ== rs=AOn4CLCV6wIbzUPwgaG-bEr_T0LNPkSzqg","width":168,"height":94},{"url":"https://i.ytimg.com/vi/HAoL5fPmgrw/hqdefault.jpg?sqp=-oaymwEXCNACELwBSFryq4qpAwkIARUAAIhCGAE= rs=AOn4CLB8-_nfanyZcaW0sA-VHNFzPVCT4Q","width":336,"height":188}]},"overlays":[{"thumbnailOverlayBadgeViewModel":{"thumbnailBadges":[{"thumbnailBadgeViewModel":{"icon":{"sources":[{"clientResource":{"imageName":"PLAYLISTS"}}]},"text":"50 videos","badgeStyle":"THUMBNAIL_OVERLAY_BADGE_STYLE_DEFAULT","backgroundColor":{"lightTheme":3355443,"darkTheme":3355443}}}],"position":"THUMBNAIL_OVERLAY_BADGE_POSITION_BOTTOM_END"}},{"thumbnailHoverOverlayViewModel":{"icon":{"sources":[{"clientResource":{"imageName":"PLAY_ALL"}}]},"text":{"content":"Play all","styleRuns":[{"startIndex":0,"length":8}]},"style":"THUMBNAIL_HOVER_OVERLAY_STYLE_COVER"}}],"backgroundColor":{"lightTheme":4144959,"darkTheme":4144959}}},"stackColor":{"lightTheme":10066329,"darkTheme":9211020}}},"metadata":{"lockupMetadataViewModel":{"title":{"content":"Linear Algebra Lectures"},"metadata":{"contentMetadataViewModel":{"metadataRows":[{"metadataParts":[{"text":{"content":"James Hamblin

#############################









Content Report
Youtor.org / YTube video Downloader © 2025

created by www.youtor.org