10 papers
Fast stability tests for Hermitian matrix polynomials
Vanni Noferini, Xuzhou Zhan
Assessing the asymptotic stability of linear self-adjoint homogeneous systems of differential-algebraic equations requires testing the Hurwitz stability of the associated Hermitian…
The Jordan canonical form of the Fréchet derivative of a matrix function and the bivariate Jordan problem
Vanni Noferini
Let be an algebraically closed field of characteristic . Given a square matrix and a polynomial , we determine…
Eventual periodicity of the Smith forms of integer matrix powers
Vanni Noferini
We prove that the Smith forms of the powers of an integer square matrix behave in an eventually periodic manner. More precisely, if denotes the Smith form of $M \i…
Rosenbrock's Theorem characterizes Prüfer domains
Vanni Noferini
Under coprimality assumptions on certain submatrices, Rosenbrock's Theorem relates the Smith form of a matrix over an elementary divisor domain to the Smith-McMil…
Nearest matrix with multiple eigenvalues by Riemannian optimization
Vanni Noferini, Lauri Nyman, Federico Poloni
Given a square complex matrix , we tackle the problem of finding the nearest matrix with multiple eigenvalues or, equivalently when had distinct eigenvalues, the nearest def…
The Smith form of Sylvester and Bézout matrices for zero-dimensional ideals
Etna Lindy, Vanni Noferini
Let be a field and let be such that the ideal is zero-dimensional. We study the Sylvester and Bézout resultant polynom…