Generalized totally nonnegative matrices

被引：6
|
作者：
Fiedler, M
Markham, TL
机构：
[1] Acad Sci Czech Republic, Inst Comp Sci, Prague 18207 8, Czech Republic
[2] Univ S Carolina, Dept Math, Columbia, SC 29208 USA
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2002年 / 345卷
关键词：
totally nonnegative matrix; ring with identity; factorization; bidiagonal matrix;
D O I：
10.1016/S0024-3795(01)00440-2
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We define a new class of generalized totally nonnegative matrices, shortly GTN-matrices, over a noncommutative ring with identity and a positive part. The class of GTN-matrices is closed under multiplication, every submatrix of a GTN-matrix is a GTN-matrix as well. We also define a standard form of a GTN-matrix. We then study the invertible GTN-matrices of a fixed order and classify them; the classes form a partially ordered set, can be (noncommutatively) multiplied and multiplication preserves ordering. (C) 2002 Elsevier Science Inc. All rights reserved.
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页码：9 / 28
页数：20
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