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A factorization of totally nonsingular matrices over a ring with identity

โœ Scribed by Miroslav Fiedler; Thomas L. Markham

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
76 KB
Volume
304
Category
Article
ISSN
0024-3795

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โœฆ Synopsis

We say that a rectangular matrix over a ring with identity is totally nonsingular (TNS) if for all k, all its relevant submatrices, either having k consecutive-rows and the first k columns, or k consecutive-columns and the first k rows, are invertible. We prove that a matrix is TNS if and only if it admits a certain factorization with bidiagonal-type factors and certain invertible entries. This approach generalizes the Loewner-Neville factorization usually applied to totally positive matrices.

๐Ÿ“œ SIMILAR VOLUMES

A Presentation for the Unipotent Group o
A Presentation for the Unipotent Group over Rings with Identity
โœ Daniel K Biss; Samit Dasgupta ๐Ÿ“‚ Article ๐Ÿ“… 2001 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 124 KB

For a ring R with identity, define Unip R to be the group of upper-triangular n matrices over R all of whose diagonal entries are 1. For i s 1, 2, . . . , n y 1, let S i denote the matrix whose only nonzero off-diagonal entry is a 1 in the ith row and ลฝ . ลฝ . i q 1 st column. Then for any integer m