Complementary basic matrices

被引：17

作者：

Fiedler, M ^{[1
]}

机构：

[1] Acad Sci Czech Republ, Inst Comp Sci, Prague 18207 8, Czech Republic

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2004年 / 384卷

关键词：

subdiagonal rank; basic matrix; zig-zag shape; factorization;

D O I：

10.1016/j.laa.2004.01.014

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show that an n x n matrix which has both subdiagonal and superdiagonal rank at most one even if we distribute the diagonal positions (except the first and last) completely between the subdiagonal and superdiagonal part, then this matrix can be factorized into a product of n - 1 matrices, each consisting of a 2 x 2 principal submatrix in two consecutive rows (and columns) in all possible of the n - 1 positions, and completed by ones along the diagonal. The converse is also true. It is shown that the spectrum does not depend on the order of the factors. (C) 2004 Elsevier Inc. All rights reserved.

引用

页码：199 / 206

页数：8