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Almost strictly sign regular rectangular matrices

P. Alonso, J. M. Peña, M. L. Serrano

TL;DR

Several properties of almost strictly sign regular rectangular matrices of maximal rank are provided and their QR factorization is analyzed.

Abstract

Almost strictly sign regular matrices are sign regular matrices with a special zero pattern and whose nontrivial minors are nonzero. In this paper we provide several properties of almost strictly sign regular rectangular matrices and analyze their QR factorization.

Almost strictly sign regular rectangular matrices

TL;DR

Several properties of almost strictly sign regular rectangular matrices of maximal rank are provided and their QR factorization is analyzed.

Abstract

Almost strictly sign regular matrices are sign regular matrices with a special zero pattern and whose nontrivial minors are nonzero. In this paper we provide several properties of almost strictly sign regular rectangular matrices and analyze their QR factorization.
Paper Structure (4 sections, 10 theorems, 39 equations)

This paper contains 4 sections, 10 theorems, 39 equations.

Table of Contents

  1. Introduction
  2. Basic notation
  3. Almost strictly sign regular rectangular matrices
  4. $QR$ factorization of ASSR matrices

Key Result

Proposition 1

Let $A$ be an $m \times n$ matrix with $\hbox{rank} (A)=r= \min \{m,n\}$. If $A$ is an ASSR and type-I staircase matrix, then any nontrivial square submatrix of $A$ is an ASSR matrix.

Theorems & Definitions (42)

  • Definition 1
  • Definition 2
  • Remark 1
  • Definition 3
  • Remark 2
  • Definition 4
  • Example 1
  • Remark 3
  • Definition 5
  • Definition 6
  • ...and 32 more