LU和CR的消除

IF 10.8 1区数学 Q1 MATHEMATICS, APPLIED

SIAM Review Pub Date : 2022-02-01 DOI:10.1137/20m1358694

G. Strang, C. Moler

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引用次数: 3

摘要

文摘行简化阶梯形rref (A)一直被用于课堂的例子:小型和低秩矩阵与整数条目r。本文创建了一个column-row rank-revealing分解= CR,与第一个独立的列在C和r非零行rref在r (A)我们要重新定义线性代数课程的开始,通过帮助学生的独立列秩和列空间。如果B包含A的前r个独立行，则这些A = CR的行产生B = W r。r × r矩阵W具有满秩r，其中B满足C。那么三重分解A = CW B以相同的方式处理A (C和B)的列和行。

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LU and CR Elimination

Abstract 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 = W R. The r by r matrix W has full rank r, where B meets C. Then the triple factorization A = CW B treats columns and rows of A (C and B) in the same way.

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来源期刊

SIAM Review 数学-应用数学

CiteScore

16.90

自引率

0.00%

发文量

期刊介绍： Survey and Review feature papers that provide an integrative and current viewpoint on important topics in applied or computational mathematics and scientific computing. These papers aim to offer a comprehensive perspective on the subject matter. Research Spotlights publish concise research papers in applied and computational mathematics that are of interest to a wide range of readers in SIAM Review. The papers in this section present innovative ideas that are clearly explained and motivated. They stand out from regular publications in specific SIAM journals due to their accessibility and potential for widespread and long-lasting influence.