Displaying similar documents to “The special circulant matrix and units in group rings.”

Bessel matrix differential equations: explicit solutions of initial and two-point boundary value problems

Enrique Navarro, Rafael Company, Lucas Jódar (1993)

Applicationes Mathematicae

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In this paper we consider Bessel equations of the type t 2 X ( 2 ) ( t ) + t X ( 1 ) ( t ) + ( t 2 I - A 2 ) X ( t ) = 0 , where A is an n × n complex matrix and X(t) is an n × m matrix for t > 0. Following the ideas of the scalar case we introduce the concept of a fundamental set of solutions for the above equation expressed in terms of the data dimension. This concept allows us to give an explicit closed form solution of initial and two-point boundary value problems related to the Bessel equation.

Determinants of (–1,1)-matrices of the skew-symmetric type: a cocyclic approach

Víctor Álvarez, José Andrés Armario, María Dolores Frau, Félix Gudiel (2015)

Open Mathematics

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An n by n skew-symmetric type (-1; 1)-matrix K =[ki;j ] has 1’s on the main diagonal and ±1’s elsewhere with ki;j =-kj;i . The largest possible determinant of such a matrix K is an interesting problem. The literature is extensive for n ≡ 0 mod 4 (skew-Hadamard matrices), but for n ≡ 2 mod 4 there are few results known for this question. In this paper we approach this problem constructing cocyclic matrices over the dihedral group of 2t elements, for t odd, which are equivalent to (-1;...

Invertibility of Matrices of Field Elements

Yatsuka Nakamura, Kunio Oniumi, Wenpai Chang (2008)

Formalized Mathematics

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In this paper the theory of invertibility of matrices of field elements (see e.g. [5], [6]) is developed. The main purpose of this article is to prove that the left invertibility and the right invertibility are equivalent for a matrix of field elements. To prove this, we introduced a special transformation of matrix to some canonical forms. Other concepts as zero vector and base vectors of field elements are also introduced as a preparation.MML identifier: MATRIX14, version: 7.9.01 4.101.1015 ...