Polynomial identities for hyper-matrices.
Tapia, Victor (2005)
Revista Colombiana de Matemáticas
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Tapia, Victor (2005)
Revista Colombiana de Matemáticas
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Furtado, Susana, Silva, Fernando C. (1998)
ELA. The Electronic Journal of Linear Algebra [electronic only]
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Michael Šebek, Vladimír Kučera (1981)
Kybernetika
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Kublanovskaya, V.N. (2005)
Zapiski Nauchnykh Seminarov POMI
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Ion Zaballa (1986)
Extracta Mathematicae
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Mohamed Boudellioua (2006)
International Journal of Applied Mathematics and Computer Science
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In this paper, we present a simple algorithm for the reduction of a given bivariate polynomial matrix to a pencil form which is encountered in Fornasini-Marchesini's type of singular systems. It is shown that the resulting matrix pencil is related to the original polynomial matrix by the transformation of zero coprime equivalence. The exact form of both the matrix pencil and the transformation connecting it to the original matrix are established.
Brawley, J.V., Mullen, Gary L. (1981)
International Journal of Mathematics and Mathematical Sciences
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Michael Cox, Kevin N. Vander Meulen, Adam Van Tuyl, Joseph Voskamp (2024)
Czechoslovak Mathematical Journal
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The Fiedler matrices are a large class of companion matrices that include the well-known Frobenius companion matrix. The Fiedler matrices are part of a larger class of companion matrices that can be characterized by a Hessenberg form. We demonstrate that the Hessenberg form of the Fiedler companion matrices provides a straight-forward way to compare the condition numbers of these matrices. We also show that there are other companion matrices which can provide a much smaller condition...
F. Acar Savaci, I. Cem Göknar (1991)
Kybernetika
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Yelena M. Smagina (2001)
Kybernetika
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A new form of the coprime polynomial fraction of a transfer function matrix is presented where the polynomial matrices and have the form of a matrix (or generalized matrix) polynomials with the structure defined directly by the controllability characteristics of a state- space model and Markov matrices , , ...