Week 3 Lesson 11 Linear Transformations theory

>> YOUR LINK HERE: ___ http://youtube.com/watch?v=TBJjmZJU_0E

This video is a premise for Linear Transformations. However, the entire video I only talk about a general transformation and not the specifics of a Linear Transformation. Misleading title, I know. • 0:00 We made it to the theory • 0:34 Remembering how functions work • 1:21 Codomain vs Range • 2:42 An example of codomain vs range • 5:31 Mapping from one space to an entirely different space • 10:13 Transformation (definition) • 12:49 Image (definition) • 13:19 Visual example of a transformation • 16:27 A matrix is the thing doing the transformation • 17:10 Example • 18:22 Notation for mapping inputs to outputs with transformations • 19:10 Relating a matrix to how functions work • 20:27 How to find the image of an input vector • 21:54 Transformations happen via matrix multiplication • 24:20 Matrix multiplication (definition) • 28:50 Matrix multiplication (worked example) • 32:18 Actually doing a transformation on a vector (worked example) • 34:31 Ax = b is back again!! (IMPORTANT)

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