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 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 of
posts 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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