Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

A Canonical Form for Max Plus Symmetric Matrices and Applications

Himadri Mukherjee, Askar Ali M

Abstract

We develop a canonical form for congruence of max plus symmetric matrices. We use the same canonical form to get results in the generalized eigenvector problem. We have also utilized the canonical form to find all symmetric matrices that commute with a given symmetric matrix.

A Canonical Form for Max Plus Symmetric Matrices and Applications

Abstract

We develop a canonical form for congruence of max plus symmetric matrices. We use the same canonical form to get results in the generalized eigenvector problem. We have also utilized the canonical form to find all symmetric matrices that commute with a given symmetric matrix.

Paper Structure

This paper contains 9 sections, 18 theorems, 52 equations.

Table of Contents

  1. Introduction
  2. Prerequisites
  3. Conjugate action and associated monoids
  4. Canonical Forms of Symmetric and Skew Symmetric matrices
  5. A little geometry
  6. Symmetric matrices
  7. Skew-symmetric matrices
  8. Applications in solving Generalised eigenvalue problem
  9. Applications to Commuting Matrices

Key Result

Theorem 1.1

Let $A \in M_n (\mathbb{T})$, and $b \in \mathbb{T^*}^n$. Then the following statements are equivalent:

Theorems & Definitions (53)

  • Definition 1.1
  • Theorem 1.1: Cunninghame-Green RA,one-sided-cunninghame
  • Example 2.1
  • Lemma 2.2
  • proof
  • Lemma 2.3
  • proof
  • Lemma 2.4
  • proof
  • Example 2.5
  • ...and 43 more