Computing tournament sequence numbers efficiently with matrix techniques.
Neuwirth, Erich (2002)
Séminaire Lotharingien de Combinatoire [electronic only]
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Neuwirth, Erich (2002)
Séminaire Lotharingien de Combinatoire [electronic only]
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Enrique Navarro, Rafael Company, Lucas Jódar (1993)
Applicationes Mathematicae
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In this paper we consider Bessel equations of the type , where A is an nn complex matrix and X(t) is an nm 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.
Karol Pąk (2008)
Formalized Mathematics
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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
Zhang, X. (2004)
Acta Mathematica Universitatis Comenianae. New Series
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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;...
Minghua Lin, Harald K. Wimmer (2014)
Special Matrices
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Companion matrices of the second type are characterized by properties that involve bilinear maps.
Gildea, Joe (2008)
Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]
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Karol Pąk (2011)
Formalized Mathematics
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We introduce linear transformations of Euclidean topological spaces given by a transformation matrix. Next, we prove selected properties and basic arithmetic operations on these linear transformations. Finally, we show that a linear transformation given by an invertible matrix is a homeomorphism.
Branko Malešević, Biljana Radičić (2012)
Kragujevac Journal of Mathematics
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Karol Pąk (2008)
Formalized Mathematics
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The paper is concerned with a generalization of concepts introduced in [13], i.e. introduced are matrices of linear transformations over a finitedimensional vector space. Introduced are linear transformations over a finitedimensional vector space depending on a given matrix of the transformation. Finally, I prove that the rank of linear transformations over a finite-dimensional vector space is the same as the rank of the matrix of that transformation.
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.