poster
2021-04-24, 17:42
http://blogs.mathworks.com/cleve/files/cab_blog_01.png
The rank of a linear transformation is a fundamental concept in linear algebra and matrix factorizations are fundamental concepts in numerical linear algebra. Gil Strang's 2020 Vision of Linear Algebra (https://ocw.mit.edu/resources/res-18-010-a-2020-vision-of-linear-algebra-spring-2020/) seeks to introduce these notions early in an introductory linear algebra course.
The CR matrix factorization provides a view of rref, the reduced row echelon form, as a rank revealing matrix factorization. I discussed CR in a pair (https://blogs.mathworks.com/cleve/2020/10/23/gil-strang-and-the-cr-matrix-factorization/) of posts (https://blogs.mathworks.com/cleve/2020/10/25/notes-on-cr-and-west0479/) in October. I now want to describe the CAB factorization, which uses rref twice in order to treat both rows and columns in the same way.
Gil and I are writing a review paper about these ideas, LU and CR Elimination. Here is a link to the current draft,
...read more >> (https://blogs.mathworks.com/cleve/?p=6589)
http://feeds.feedburner.com/~r/mathworks/moler/~4/T7Xz1mFRWXY
More... (http://feedproxy.google.com/~r/mathworks/moler/~3/T7Xz1mFRWXY/)
The rank of a linear transformation is a fundamental concept in linear algebra and matrix factorizations are fundamental concepts in numerical linear algebra. Gil Strang's 2020 Vision of Linear Algebra (https://ocw.mit.edu/resources/res-18-010-a-2020-vision-of-linear-algebra-spring-2020/) seeks to introduce these notions early in an introductory linear algebra course.
The CR matrix factorization provides a view of rref, the reduced row echelon form, as a rank revealing matrix factorization. I discussed CR in a pair (https://blogs.mathworks.com/cleve/2020/10/23/gil-strang-and-the-cr-matrix-factorization/) of posts (https://blogs.mathworks.com/cleve/2020/10/25/notes-on-cr-and-west0479/) in October. I now want to describe the CAB factorization, which uses rref twice in order to treat both rows and columns in the same way.
Gil and I are writing a review paper about these ideas, LU and CR Elimination. Here is a link to the current draft,
...read more >> (https://blogs.mathworks.com/cleve/?p=6589)
http://feeds.feedburner.com/~r/mathworks/moler/~4/T7Xz1mFRWXY
More... (http://feedproxy.google.com/~r/mathworks/moler/~3/T7Xz1mFRWXY/)