Five Factorizations of a Matrix

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A Vision of Linear Algebra Instructor: Gilbert Strang View the complete course: https://ocw.mit.edu/2020-vision YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP61iQEFiWLE21EJCxwmWvvek In this video, Professor Strang provides an overall look at linear algebra by highlighting five different ways that a matrix gets factored. For every matrix A, four key vector spaces are the row space and nullspace of A and its transpose. To compute with A, we factor it into A = (column space basis) times (row space basis). The simplest basis uses independent columns taken directly from the matrix A. The best bases of all use *orthogonal* vectors from the column space and the row space of A. These “singular vectors” produce the great Singular Value Decomposition! License: Creative Commons BY-NC-SA More information at https://ocw.mit.edu/terms More courses at https://ocw.mit.edu We encourage constructive comments and discussion on OCW’s YouTube and other social media channels. Personal attacks, hate speech, trolling, and inappropriate comments are not allowed and may be removed. More details at https://ocw.mit.edu/comments.

Published 2023-12-06 · Watch on YouTube ↗
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