Froilán M. Dopico

activity

20232026

most citedOn bundle closures of matrix pencils and matrix polynomials

1 citations · 1 across the 11 of their papers we have counts for

collaborators

12 papers

math.NA2026

Generic factorizations and alternating direction method for fixed-rank approximation of matrix polynomials

Sweta Das, Andrii Dmytryshyn, Froilán M. Dopico +1

We present an algorithm for approximating a given matrix polynomial of degree $d$ by a matrix polynomial of prescribed rank and degree at most $d$ . The method builds on recent adva…

math.NA2026

Distance to nearest skew-symmetric matrix polynomials of bounded rank

Andrii Dmytryshyn, Froilán M. Dopico, Rakel Hellberg

We propose an algorithm that approximates a given matrix polynomial of degree $d$ by another skew-symmetric matrix polynomial of a specified rank and degree at most $d$ . The algori…

math.SP2026

Generic real Jordan canonical forms

Fernando De Terán, Froilán M. Dopico

We obtain the generic real Jordan canonical forms for $n \times n$ matrices with real entries. More precisely, we prove that the set of $n \times n$ real matrices is the union of the…

math.SP2025

The generic canonical form for $^{⋆}$ congruence of matrices

Fernando De Terán, Froilán M. Dopico

First, we prove that the set of $n \times n$ complex matrices is the closure of a certain open subset whose elements have a very specific canonical form under congruence, which is u…

math.SP2025

Real-congruence canonical forms of real matrices

Fernando De Terán, Froilán M. Dopico

We present two new canonical forms for real congruence of a real square matrix $A$ . The first one is a direct sum of canonical matrices of four different types and is obtained from…

math.SP2025

On the dimension of orbits of matrix pencils under strict equivalence

Fernando De Terán, Froilán M. Dopico, Patryk Pagacz

We prove that, given two matrix pencils $L$ and $M$ , if $M$ belongs to the closure of the orbit of $L$ under strict equivalence, then the dimension of the orbit of $M$ is smaller t…

math.SP2025

Polynomial and rational matrices with the invariant rational functions and the four sequences of minimal indices prescribed

Itziar Baragaña, Froilán M. Dopico, Silvia Marcaida +1

The complete eigenstructure, or structural data, of a rational matrix $R (s)$ is comprised by its invariant rational functions, both finite and at infinity, which in turn determine…

math.NA2024

Para-Hermitian rational matrices

Froilán Dopico, Vanni Noferini, María C. Quintana +1

In this paper we study para-Hermitian rational matrices and the associated structured rational eigenvalue problem (REP). Para-Hermitian rational matrices are square rational matric…

math.RA2024

Rosenbrock's Theorem on System Matrices over Elementary Divisor Domains

Froilán Dopico, Vanni Noferini, Ion Zaballa

Rosenbrock's theorem on polynomial system matrices is a classical result in linear systems theory that relates the Smith-McMillan form of a rational matrix $G$ with the Smith forms…

math.NA2024★ 1 cited

On bundle closures of matrix pencils and matrix polynomials

Fernando De Terán, Froilán M. Dopico, Vadym Koval +1

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…

math.RT2023

Even grade generic skew-symmetric matrix polynomials with bounded rank

Fernando De Terán, Andrii Dmytryshyn, Froilán M. Dopico

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 $2 r$ is the closure of the…

math.NA2023

Minimal rank factorizations of polynomial matrices

Andrii Dmytryshyn, Froilán Dopico, Paul Van Dooren

We investigate rank revealing factorizations of $m \times n$ polynomial matrices $P (λ)$ into products of three, $P (λ) = L (λ) E (λ) R (λ)$ , or two, $P (λ) = L (λ) R (λ)$ , polynomial matr…

Generic factorizations and alternating direction method for fixed-rank approximation of matrix polynomials

Distance to nearest skew-symmetric matrix polynomials of bounded rank

Generic real Jordan canonical forms

The generic canonical form for ⋆congruence of matrices

Real-congruence canonical forms of real matrices

On the dimension of orbits of matrix pencils under strict equivalence

Polynomial and rational matrices with the invariant rational functions and the four sequences of minimal indices prescribed

Para-Hermitian rational matrices

Rosenbrock's Theorem on System Matrices over Elementary Divisor Domains

On bundle closures of matrix pencils and matrix polynomials

Even grade generic skew-symmetric matrix polynomials with bounded rank

Minimal rank factorizations of polynomial matrices

The generic canonical form for $^{⋆}$ congruence of matrices