Displaying similar documents to “Block Diagonal 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

Similarity:

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;...

Examples Illustrating some Aspects of the Weak Deligne-Simpson Problem

Kostov, Vladimir (2001)

Serdica Mathematical Journal

Similarity:

Research partially supported by INTAS grant 97-1644 We consider the variety of (p + 1)-tuples of matrices Aj (resp. Mj ) from given conjugacy classes cj ⊂ gl(n, C) (resp. Cj ⊂ GL(n, C)) such that A1 + . . . + A[p+1] = 0 (resp. M1 . . . M[p+1] = I). This variety is connected with the weak Deligne-Simpson problem: give necessary and sufficient conditions on the choice of the conjugacy classes cj ⊂ gl(n, C) (resp. Cj ⊂ GL(n, C)) so that there exist (p + 1)-tuples with trivial...

Invertibility of Matrices of Field Elements

Yatsuka Nakamura, Kunio Oniumi, Wenpai Chang (2008)

Formalized Mathematics

Similarity:

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 ...

Toeplitz matrices and convergence

Heike Mildenberger (2000)

Fundamenta Mathematicae

Similarity:

We investigate | | χ 𝔸 , 2 | | , the minimum cardinality of a subset of 2 ω that cannot be made convergent by multiplication with a single matrix taken from 𝔸 , for different sets 𝔸 of Toeplitz matrices, and show that for some sets 𝔸 it coincides with the splitting number. We show that there is no Galois-Tukey connection from the chaos relation on the diagonal matrices to the chaos relation on the Toeplitz matrices with the identity on 2 ω as first component. With Suslin c.c.c. forcing we show that | | χ 𝕄 , 2 | | <...

Determinant evaluations for binary circulant matrices

Christos Kravvaritis (2014)

Special Matrices

Similarity:

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.

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

Enrique Navarro, Rafael Company, Lucas Jódar (1993)

Applicationes Mathematicae

Similarity:

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.

Solutions of Linear Equations

Karol Pąk (2008)

Formalized Mathematics

Similarity:

In this paper I present the Kronecker-Capelli theorem which states that a system of linear equations has a solution if and only if the rank of its coefficient matrix is equal to the rank of its augmented matrix.MML identifier: MATRIX15, version: 7.8.09 4.97.1001