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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.

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

88%

Ye G.

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.