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Companion matrices and their relations to Toeplitz and Hankel matrices

100%

Luo Y. , Hill R.

tom 3

nr 1

In this paper we describe some properties of companion matrices and demonstrate some special patterns that arisewhen a Toeplitz or a Hankel matrix is multiplied by a related companion matrix.We present a necessary and sufficient condition, generalizing known results, for a matrix to be the transforming matrix for a similarity between a pair of companion matrices. A special case of our main result shows that a Toeplitz or a Hankel matrix can be extended using associated companion matrices, preserving the Toeplitz or Hankel structure respectively.

Eigenvalues of 2-tridiagonal Toeplitz matrix

100%

Borowska J. , Łacińska L.

Journal of Applied Mathematics and Computational Mechanics

2015

tom Vol. 14, nr 4

11--17

In this article an explicit formula for eigenvalues of a 2-tridiagonal Toeplitz matrix can be derived on the basis of a certain relation between the determinant of this matrix and the determinant of a pertinent tridiagonal matrix. It can be pointed out that the problem is investigated without imposing any conditions on the elements of matrix.

Another Constructed Chaotic Image Encryption Scheme Based on Toeplitz Matrix and Hankel Matrix

88%

Ye G.

2010

tom Vol. 101, nr 4

321-333

This paper presents a novel image encryption scheme based on Toeplitz matrix and Hankel matrix. According to the definition and the expression of Toeplitz matrix and Hankel matrix, we permutate the positions of image pixels to confuse the relationship between the plain-image and cipher-image, and construct a new key. To enhance security further, hyper-chaos system of L¨u and Chen is taken to change the grey distribution of image pixels simultaneously. Numerical experimental results demonstrate that the key space is large enough, and the key is sensitive to initial conditions to resist the brute-force attack in the proposed scheme. Additionally, the distribution of grey values in encrypted image has a random-like behavior to resist statistical analysis. The proposed encryption scheme in this paper can suggest a high secure and efficient way for real-time image encryption and transmission in practice.

Unitary automorphisms of the space of Toeplitz-plus-Hankel matrices

75%

Abdikalykov A. K. , Chugunov V. N. , Ikramov K. D.

tom 3

nr 1

Our motivation was a paper of 1991 indicating three special unitary matrices that map Hermitian Toeplitz matrices by similarity into real Toeplitz-plus-Hankel matrices. Generalizing this result, we give a complete description of unitary similarity automorphisms of the space of Toeplitz-plus-Hankel matrices.

Recurrence form for determinant of a heptadiagonal symmetric Toeplitz matrix

75%

Borowska J. , Łacińska L.

2014

tom Vol. 13, nr 4

19--26

In this paper we show that the determinant of heptadiagonal symmetric Toeplitz matrix can be represented by a particular solution of the system of three homogeneous linear recurrence equations. The general considerations are illustrated by certain numerical example implementated in the Maple system.

A numerical algorithm for computing the inverse of a Toeplitz pentadiagonal matrix

63%

Talibi B. , Hadj D. A. , Sarsri D.

Journal of Applied Mathematics and Computational Mechanics

2018

tom Vol. 17, nr 3

83--95

In the current paper, we present a computationally efficient algorithm for obtaining the inverse of a pentadiogonal toeplitz matrix. Few conditions are required, and the algorithm is suited for implementation using computer algebra systems.

On a recurrence for permanents of a sequence of 3-tridiagonal matrices

63%

Trojovský P. , Zvoníková I.

tom Vol. 18, nr 4

95--100

This is a corrigendum of the paper: Küçük, A. Z. & Düz, M. (2017). Relationships between the permanents of a certain type of k-tridiagonal symmetric Toeplitz and the Chebyshev polynomials. Journal of Applied Mathematics and Computational Mechanics, 16, 75-86. We will show that Remark 9, on page 84, does not hold, what is the consequence of the incorrect proof, which authors formulated there.