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Palindromic linearizations of a matrix polynomial of odd degreee obtained from Fiedler pencils with repetition
Many applications give rise to structured, in particular T- palindromic, matrix polynomials. In order to solve a polynomial eigenvalue problem P(�)x = 0, where P(�) is a T-palindromic matrix… Expand
Large vector spaces of block-symmetric strong linearizations of matrix polynomials
Abstract Given a matrix polynomial P ( λ ) = ∑ i = 0 k λ i A i of degree k , where A i are n × n matrices with entries in a field F , the development of linearizations of P ( λ ) that preserve… Expand
Structured strong linearizations from Fiedler pencils with repetition II
Abstract In this paper we give strong linearizations of a matrix polynomial P ( λ ) preserving the skew-symmetry or T-alternating structure of P ( λ ) . The linearizations obtained are of the form S… Expand
Linearizations of Hermitian Matrix Polynomials Preserving the Sign Characteristic
- María Isabel Bueno Cachadina, F. Dopico, S. Furtado
- Computer Science, Mathematics
- SIAM J. Matrix Anal. Appl.
- 24 August 2015
The development of strong linearizations preserving whatever structure a matrix polynomial might possess has been a very active area of research in the last years, since such linearizations are the starting point of numerical algorithms for computing eigenvalues of structured matrix poyllomials with the properties imposed by the considered structure. Expand
Spectral variation under congruence
In this paper we study the possible spectra among matrices congruent to a given AεMn (C). It is important to distinguish singular A from nonsingular and, among non-singular matrices, to distinguish… Expand
Structured distance to normality of tridiagonal matrices
Abstract In this article we study the distance d , measured in the Frobenius norm, of a tridiagonal matrix T to the set I T of similarly structured irreducible normal matrices. The matrices in the… Expand
A block-symmetric linearization of odd degree matrix polynomials with optimal eigenvalue condition number and backward error
The standard way of solving numerically a polynomial eigenvalue problem (PEP) is to use a linearization and solve the corresponding generalized eigenvalue problem (GEP). In addition, if the PEP… Expand
Minimal matrices in the Bruhat order for symmetric (0,1)-matrices
Abstract In this paper we study the minimal matrices for the Bruhat order on the class of symmetric ( 0 , 1 ) -matrices with given row sum vector. We will show that, when restricted to the symmetric… Expand
On the Bruhat order of labeled graphs
- R. Brualdi, Rosário Fernandes, S. Furtado
- Mathematics, Computer Science
- Discret. Appl. Math.
- 15 April 2019
We investigate two Bruhat (partial) orders on graphs with vertices labeled 1 , 2 , … , n and with a specified degree sequence R . Expand
Products of matrices with prescribed spectra and ranks
This paper studies the possibility of writing a given square matrix as the product of two matrices with prescribed spectra and ranks. It extends some previously known results.