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pro vyhledávání: '"de Terán, Fernando"'
Bundles of matrix polynomials are sets of matrix polynomials with the same size and grade and the same eigenstructure up to the specific values of the eigenvalues. It is known that the closure of the bundle of a pencil $L$ (namely, a matrix polynomia
Externí odkaz:
http://arxiv.org/abs/2402.16702
We show that the set of $m \times m$ complex skew-symmetric matrix polynomials of even 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 with certain, explicitly described, c
Externí odkaz:
http://arxiv.org/abs/2312.16672
We obtain the generic complete eigenstructures of complex Hermitian $n\times n$ matrix pencils with rank at most $r$ (with $r\leq n$). To do this, we prove that the set of such pencils is the union of a finite number of bundle closures, where each bu
Externí odkaz:
http://arxiv.org/abs/2209.10495
In this paper, which is a follow-up to [A. Borobia, R. Canogar, F. De Ter\'an, Mediterr. J. Math. 18, 40 (2021)], we provide a necessary and sufficient condition for the matrix equation $X^\top AX=B$ to be consistent when $B$ is symmetric. The condit
Externí odkaz:
http://arxiv.org/abs/2209.02312
Autor:
De Terán, Fernando, Dopico, Froilán M.
Bundles of matrix pencils (under strict equivalence) are sets of pencils having the same Kronecker canonical form, up to the eigenvalues (namely, they are an infinite union of orbits under strict equivalence). The notion of bundle for matrix pencils
Externí odkaz:
http://arxiv.org/abs/2204.10237
Publikováno v:
In Linear Algebra and Its Applications 1 December 2024 702:218-239
Given a bilinear form on $\mathbb C^n$, represented by a matrix $A\in\mathbb C^{n\times n}$, the problem of finding the largest dimension of a subspace of $\mathbb C^n$ such that the restriction of $A$ to this subspace is a non-degenerate skew-symmet
Externí odkaz:
http://arxiv.org/abs/2203.07100
In the framework of Polynomial Eigenvalue Problems, most of the matrix polynomials arising in applications are structured polynomials (namely (skew-)symmetric, (skew-)Hermitian, (anti-)palindromic, or alternating). The standard way to solve Polynomia
Externí odkaz:
http://arxiv.org/abs/2010.06033
We determine the generic complete eigenstructures for $n \times n$ complex symmetric matrix polynomials of odd grade $d$ and rank at most $r$. More precisely, we show that the set of $n \times n$ complex symmetric matrix polynomials of odd grade $d$,
Externí odkaz:
http://arxiv.org/abs/1911.01408
The generic change of the Weierstrass Canonical Form of regular complex structured matrix pencils under generic structure-preserving additive low-rank perturbations is studied. Several different symmetry structures are considered and it is shown that
Externí odkaz:
http://arxiv.org/abs/1902.00444