Karol Pąk (2008)
Formalized Mathematics
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In this paper I present basic properties of block diagonal matrices over a set. In my approach the finite sequence of matrices in a block diagonal matrix is not restricted to square matrices. Moreover, the off-diagonal blocks need not be zero matrices, but also with another arbitrary fixed value.
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.
Carla Dionisi (2004)
Revista Matemática Complutense
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In this paper nondegenerate multidimensional matrices of boundary format in V ⊗ ... ⊗ V are investigated by their link with Steiner vector bundles on product of projective spaces. For any nondegenerate matrix A the stabilizer for the SL(V) x ... x SL(V)-action, Stab(A), is completely described. In particular we prove that there exists an explicit action of SL(2) on V ⊗ ... ⊗ V such that Stab(A) ⊆ SL(2) and the equality holds if and only if A belongs to a unique SL(V) x ... x SL(V)-orbit...
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.
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 ...
De, Dibyendu, Paul, Ram Krishna (2011)
The New York Journal of Mathematics [electronic only]
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J. Dorsey, C.R. Johnson, Z. Wei (2014)
Special Matrices
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Identified are certain special periodic diagonal matrices that have a predictable number of paired eigenvalues. Since certain symmetric Toeplitz matrices are special cases, those that have several multiple 5 eigenvalues are also investigated further. This work generalizes earlier work on response matrices from circularly symmetric models.
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.
Jan Hauke, Augustyn Markiewicz (1994)
Applicationes Mathematicae
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The partial ordering induced by the Loewner partial ordering on the convex cone comprising all matrices which multiplied by a given positive definite matrix become nonnegative definite is considered. Its relation to orderings which are induced by the Loewner partial ordering of the squares of matrices is presented. Some extensions of the latter orderings and their comparison to star orderings are given.