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Product of rectangular Toeplitz (Hankel) matrices

Said Bensliman, Ameur Yagoub, Kamel Toumache

Abstract

In this paper, we study products of asymmetric Toeplitz matrices, we give necessary and sufficient conditions for the product of two asymmetric Toeplitz matrices compatible sizes is asymmetric Toeplitz matrix. We also give some results related to the isometry.

Product of rectangular Toeplitz (Hankel) matrices

Abstract

In this paper, we study products of asymmetric Toeplitz matrices, we give necessary and sufficient conditions for the product of two asymmetric Toeplitz matrices compatible sizes is asymmetric Toeplitz matrix. We also give some results related to the isometry.
Paper Structure (4 sections, 16 theorems, 28 equations)

This paper contains 4 sections, 16 theorems, 28 equations.

Table of Contents

  1. Introduction.
  2. Preliminaries.
  3. product of two matrices in $\mathcal{T}(n,m)$.
  4. isometry of asymmetric Toeplitz (Hankel) matrix

Key Result

Lemma 2.1

Let $A\in\mathcal{T}(n,m)$. Then

Theorems & Definitions (36)

  • Lemma 2.1
  • proof
  • Lemma 2.2
  • proof
  • Remark 2.3
  • Lemma 2.4
  • proof
  • Lemma 2.5
  • Lemma 2.6
  • proof
  • ...and 26 more