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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 and , if belongs to the closure of the orbit of under strict equivalence, then the dimension of the orbit of is smaller t…
math.SP2024
The Taylor spectrum of pairs of isometries
Zbigniew Burdak, Patryk Pagacz
In the paper we fully describe Taylor spectrum of pairs of isometries given by diagrams. In most cases both isometries in such pairs have non-trivial shift part and its Taylor spec…
math.SP2024
On singular pencils with commuting coefficients
Vadym Koval, Patryk Pagacz
We investigate the relation between the spectrum of matrix (or operator) polynomials and the Taylor spectrum of its coefficients. We prove that the polynomial of commuting matrices…