Geometry of Matrix Polynomial Spaces
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DOI: 10.1007/s10208-019-09423-1
Abstract: We study how small perturbations of general matrix polynomials may change their elementary divisors and minimal indices by constructing the closure hierarchy (stratification) graphs of matrix polynomials’ orbits and bundles. To solve this problem, we… read more here.
Keywords: fiedler; geometry; matrix polynomials; matrix polynomial ... See more keywords
Certain Generating Matrix Relations of Generalized Bessel Matrix Polynomials from the View Point of Lie Algebra Method
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DOI: 10.1007/s41980-018-0067-0
Abstract: The main objective of the present paper is to derive the integral representation, matrix recurrence relations and matrix differential recurrence relations for the generalized Bessel matrix polynomials. Furthermore, we obtain a class of generating matrix… read more here.
Keywords: generalized bessel; matrix; relations generalized; matrix polynomials ... See more keywords
Generic skew-symmetric matrix polynomials with fixed rank and fixed odd grade
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DOI: 10.1016/j.laa.2017.09.006
Abstract: We show that the set of m×m complex skew-symmetric matrix polynomials of odd grade d, i.e., of degree at most d, and (normal) rank at most 2r is the closure of the single set of matrix polynomials ... read more here.
Keywords: symmetric matrix; skew symmetric; matrix; odd grade ... See more keywords
Algebraic linearizations of matrix polynomials
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DOI: 10.1016/j.laa.2018.10.028
Abstract: We show how to construct linearizations of matrix polynomials $z\mathbf{a}(z)\mathbf{d}_0 + \mathbf{c}_0$, $\mathbf{a}(z)\mathbf{b}(z)$, $\mathbf{a}(z) + \mathbf{b}(z)$ (when $\mathrm{deg}\left(\mathbf{b}(z)\right) < \mathrm{deg}\left(\mathbf{a}(z)\right)$), and $z\mathbf{a}(z)\mathbf{d}_0\mathbf{b}(z) + \mathbf{c_0}$ from linearizations of the component parts, $\mathbf{a}(z)$ and $\mathbf{b}(z)$. This allows… read more here.
Keywords: algebraic linearizations; linearizations matrix; mathbf; matrix polynomials ... See more keywords