On the characteristic polynomial of matrices with prescribed columns and the stabilization and observability of linear systems.
Furtado, Susana, Silva, Fernando C. (1998)
ELA. The Electronic Journal of Linear Algebra [electronic only]
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Displaying similar documents to “Separable characteristic polynomials of pencils and property .”
On the characteristic polynomial of matrices with prescribed columns and the stabilization and observability of linear systems.
An equivalent matrix pencilfor bivariate polynomial matrices
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.
Determination of matrices of the desired 2-D characteristic polynomial
T. Kaczorek, M. Świerkosz (1988)
Applicationes Mathematicae
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Remarks on inverse of matrix polynomials
Fischer, Cyril, Náprstek, Jiří
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Analysis of a non-classically damped engineering structure, which is subjected to an external excitation, leads to the solution of a system of second order ordinary differential equations. Although there exists a large variety of powerful numerical methods to accomplish this task, in some cases it is convenient to formulate the explicit inversion of the respective quadratic fundamental system. The presented contribution uses and extends concepts in matrix polynomial theory and proposes...
Algorithms. 38. CHARPOL. Computation of the characteristic polynomial of matrices
Pavla Holasová (1975)
Aplikace matematiky
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Discrete-time symmetric polynomial equations with complex coefficients
Didier Henrion, Jan Ježek, Michael Šebek (2002)
Kybernetika
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Discrete-time symmetric polynomial equations with complex coefficients are studied in the scalar and matrix case. New theoretical results are derived and several algorithms are proposed and evaluated. Polynomial reduction algorithms are first described to study theoretical properties of the equations. Sylvester matrix algorithms are then developed to solve numerically the equations. The algorithms are implemented in the Polynomial Toolbox for Matlab.
Matrix quadratic equations column/row reduced factorizations and an inertia theorem for matrix polynomials
Irina Karelin, Leonid Lerer (2001)
International Journal of Applied Mathematics and Computer Science
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It is shown that a certain Bezout operator provides a bijective correspondence between the solutions of the matrix quadratic equation and factorizatons of a certain matrix polynomial (which is a specification of a Popov-type function) into a product of row and column reduced polynomials. Special attention is paid to the symmetric case, i.e. to the Algebraic Riccati Equation. In particular, it is shown that extremal solutions of such equations correspond to spectral factorizations of...