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LU and CR Elimination

The reduced row echelon form rref(A) has traditionally been used for classroom examples: small matrices A with integer entries and low rank r. This paper creates a column-row rank-revealing factorization A=CR, with the first r independent columns of A in C and the r nonzero rows of rref(A) in R. We want to reimagine the start of a linear algebra course by helping students to see the independent columns of A and the rank and the column space. If B contains the first r independent rows of A, then those rows of A=CR produce B=WR. The r by r matrix W has full rank r, where B meets C. Then the triple factorization A=CW−1B treats columns and rows of A (C and B) in the same way.

Ketersediaan

Informasi Detail

Judul Seri

SIAM REVIEW; Vol.64 No.1 March 2022

No. Panggil

-

Penerbit

: .,

Deskripsi Fisik

p. 181-190

Bahasa

English

ISBN/ISSN

-

Klasifikasi

NONE

Tipe Isi

-

Tipe Media

-

Tipe Pembawa

-

Edisi

-

Subjek

FACTORIZATION
MATRIX
ELIMINATION
RANK
ROW ECHELON FORM

Info Detail Spesifik

https://doi.org/10.1137/20M1358694

Pernyataan Tanggungjawab

Gilbert Strang, Cleve Moler

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