CR and CAB, Rank Revealing Matrix Factorizations - Cleve Moler on Mathematics and Computing
 

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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 [URL="https://ocw.mit.edu/resources/res-18-010-a-2020-vision-of-linear-algebra-spring-2020/"]2020 Vision of Linear Algebra[/URL] 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 [URL="https://blogs.mathworks.com/cleve/2020/10/23/gil-strang-and-the-cr-matrix-factorization/"]pair[/URL] of [URL="https://blogs.mathworks.com/cleve/2020/10/25/notes-on-cr-and-west0479/"]posts[/URL] 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,



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