Displaying similar documents to “Determinants of (–1,1)-matrices of the skew-symmetric type: a cocyclic approach”

Determinant evaluations for binary circulant matrices

Christos Kravvaritis (2014)

Special Matrices

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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

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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.

Characterization and properties of (Pσ, Q) symmetric and co-symmetric matrices

William F. Trench (2014)

Special Matrices

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Let P ∈ ℂmxm and Q ∈ ℂn×n be invertible matrices partitioned as P = [P0 P1 · · · Pk−1] and Q = [Q0 Q1 · · · Qk−1], with P ℓ ∈ ℂm×mℓ and Qℓ ∈ ℂn×nℓ , 0 ≤ ℓ ≤ k − 1. Partition P−1 and Q−1 as [...] where P̂ℓ ∈ ℂmℓ ×m, Q̂ℓ ∈ ℂnℓ×n , P̂ℓPm = δℓmImℓ , and Q̂ℓQm = δℓmInℓ , 0 ≤ ℓ, m ≤ k − 1. Let Zk = {0, 1, . . . , k − 1}. We study matrices A = [...] Pσ(ℓ)FℓQℓ and B = [...] QℓGℓPσ(ℓ), where σ : Zk → Zk. Special cases: A = [...] and B = [...] , where Aℓ ∈ ℂd1×d2 and Bℓ ∈ ℂd2×d1, 0 ≤ ℓ ≤ k − 1. ...