Elimination and Factorization A = CR
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
If a matrix A has rank r, then its row echelon form (after elimination) contains the identity matrix in its first r independent columns. How do we interpret the matrix F that appears in the remaining n−r columns of that echelon form? F multiplies those first r independent columns of A to give its n−r dependent columns. Then F reveals bases for the row space and the nullspace of the original matrix A. And F is the key to the column-row factorization A = CR
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.
Instructor: Gilbert Strang
View the complete course: https://ocw.mit.edu/2020-vision
YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP61iQEFiWLE21EJCxwmWvvek
If a matrix A has rank r, then its row echelon form (after elimination) contains the identity matrix in its first r independent columns. How do we interpret the matrix F that appears in the remaining n−r columns of that echelon form? F multiplies those first r independent columns of A to give its n−r dependent columns. Then F reveals bases for the row space and the nullspace of the original matrix A. And F is the key to the column-row factorization A = CR
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.
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