Multiple LU factorizations of a singular matrix

被引：6

作者：

Dopico, Froilan M.

Johnson, Charles R.

Molera, Juan M.

机构：

[1] Univ Carlos III Madrid, Dept Matemat, Leganes 28911, Spain

[2] Coll William & Mary, Dept Math, Williamsburg, VA 23187 USA

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2006年 / 419卷 / 01期

关键词：

canonical form; LU factorization; minors; singular matrices;

D O I：

10.1016/j.laa.2006.03.043

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A singular matrix A may have more than one LU factorizations. In this work the set of all LU factorizations of A is explicitly described when the lower triangular matrix L is nonsingular. To this purpose, a canonical form of A under left multiplication by unit lower triangular matrices is introduced. This canonical form allows us to characterize the matrices that have an LU factorization and to parametrize all possible LU factorizations. Formulae in terms of quotient of minors of A are presented for the entries of this canonical form. (c) 2006 Elsevier Inc. All rights reserved.

引用

页码：24 / 36

页数：13

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