Advanced Linear Algebra Lecture 26 The CayleyHamilton Theorem

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We learn about the Cayley-Hamilton theorem, which says that every matrix, when plugged into its own characteristic polynomial, produces the zero matrix. As a consequence, all powers of a matrix live in some n-dimension subspace of the n^2-dimensional space of n-by-n matrices. • Textbook: http://www.njohnston.ca/publications/... • Blank course notes (lectures 25-29): http://www.njohnston.ca/ala_week7.pdf • Annotated course notes (lectures 25-29): http://www.njohnston.ca/ala_week7_ann... • Please leave a comment below if you have any questions, comments, or corrections.

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