Special Matrices Volume 2 Issue 2014 -

Special Matrices

Volume 2 Issue 2014 -

Contents
Journal Overview

Immanant Conversion on Symmetric Matrices

M. Purificação Coelho, M. Antónia Duffner, Alexander E. Guterman February 12, 2014 Page range: 1-10

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Abstract

Let ∑ n (ℂ) denote the space of all n × n symmetric matrices over the complex field ℂ. The main objective of this paper is to prove that the maps Φ : ∑ n (ℂ) → ∑ n (ℂ) satisfying for any fixed irreducible characters χ, χ ': Sn → ℂ the condition d χ (A+αB) = d χ ' (Φ(A)+αΦ(B)) for all matrices A, B ∈ ∑ n (ℂ) and all scalars α ∈ ℂ are automatically linear and bijective. As a corollary of the above result we characterize all such maps Φ acting on ∑ n (ℂ).

Cayley-Hamilton theorem for left eigenvalues of 3 × 3 quaternionic matrices

E. Macías-Virgós, M. J. Pereira-Sáez March 20, 2014 Page range: 11-18

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Abstract

We prove that any quaternionic matrix of order n ≤ 3 admits a characteristic function, whose roots are the left eigenvalues, that satisfies Cayley-Hamilton theorem.

About this journal

Special Matrices publishes original articles of wide significance and originality in all areas of research involving structured matrices present in various branches of pure and applied mathematics and their noteworthy applications in physics, engineering, and other sciences.

Scope

Matrix theory
Spectral graph theory
Combinatorial matrix theory
Nonnegative matrices
Inequalities in matrices
Numerical matrix theory
Operator theory and matrices