相关论文: Some notes about matrices, 4

These notes concern linear transformations on R^n and C^n, exponentials of linear transformations, and some related geometric questions.

In this paper we have discussed different possible orthogonalities in matrices, namely orthogonal, quasi-orthogonal, semi-orthogonal and non-orthogonal matrices including completely positive matrices, while giving some of their…

In these notes we explore a variety of models comprising a large number of constituents. An emphasis is placed on integrals over large Hermitian matrices, as well as quantum mechanical models whose degrees of freedom are organised in a…

We associate with a matrix over an arbitrary field an infinite family of matrices whose sizes vary from one to infinity; their entries are traces of powers of the original matrix. We explicitly evaluate the determinants of matrices in our…

This brief note concerns the invertibility of certain alternant matrices. In particular those that consisting of polynomials and products of polynomials and logarithms are shown to be invertible under appropriate conditions on the degrees…

This paper is concentrated on the classification of permutation matrix with the permutation similarity relation, mainly about the canonical form of a permutational similar equivalence class, the cycle matrix decomposition of a permutation…

These notes deal with algebras equipped with an involution and related matters.

Matrices over the dual numbers are considered. We propose an approach to classify these matrices up to similarity. Some preliminary results on the realization of this approach are obtained. In particular, we produce explicitly canonical…

We present in this paper some fundamental tools for developing matrix analysis over the complex quaternion algebra. As applications, we consider generalized inverses, eigenvalues and eigenvectors, similarity, determinants of complex…

We define recurrence matrices and study a few properties (links with automatic sequences, branch groups etc.) of them.

This note presents several conditions to characterize real matrix similarity between a Hurwitz matrix (and then more generally, a real square matrix) and a diagonal dominant matrix.

This paper has an expository nature. We compare the spectral properties (such as boundedness and compactness) of three families of semi-infinite matrices and point out similarities between them. The common feature of these families is that…

Here we briefly discuss lattices in Euclidean spaces and spaces of lattices, which are basic objects that can be described in terms of matrices and are important settings in classical analysis.

New cases of the multiplicity conjecture are considered.

A new class of structured matrices is presented and a closed form formula for their determinant is established. This formula has strong connections with the one for Vandermonde matrices.

In this short paper, we study some trace inequalities of the products of the matrices and the power of matrices by the use of elementary calculations.

In this study, we introduce the concept of commutative quaternions and commutative quaternion matrices. Firstly, we give some properties of commutative quaternions and their Hamilton matrices. After that we investigate commutative…

This is about algebras of complex $n\times n$ matrices. Do these algebras look similar for all large $n$? This paper is intended for general audience.

We classify the matrices M which correspond to finite categories

We construct new, previously unknown parametric families of complex conference matrices and of complex Hadamard matrices of square orders and related them to complex equiangular tight frames.