Displaying similar documents to “Bilinear characterizations of companion matrices”

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


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;...

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

Enrique Navarro, Rafael Company, Lucas Jódar (1993)

Applicationes Mathematicae


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.

Determinant evaluations for binary circulant matrices

Christos Kravvaritis (2014)

Special Matrices


Determinant formulas for special binary circulant matrices are derived and a new open problem regarding the possible determinant values of these specific circulant matrices is stated. The ideas used for the proofs can be utilized to obtain more determinant formulas for other binary circulant matrices, too. The superiority of the proposed approach over the standard method for calculating the determinant of a general circulant matrix is demonstrated.