Publication: Quasi-triangularization of matrix polynomials over arbitrary fields
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2023-05-15
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Elsevier
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Abstract
In [19], Taslaman, Tisseur, and Zaballa show that any regular matrix polynomial P (λ)over an algebraically closed field is spectrally equivalent to a triangular matrix polynomial of the same degree. When P (λ)is real and regular, they also show that there is a real quasi-triangular matrix polynomial of the same degree that is spectrally equivalent to P (λ), in which the diagonal blocks are of size at most 2 × 2. This paper generalizes these results to regular matrix polynomials P (λ)over arbitrary fields F, showing that any such P (λ) can be quasi-triangularized to a spectrally equivalent matrix polynomial over F of the same degree, in which the largest diagonal block size is bounded by the highest degree appearing among all of the F-irreducible factors in the Smith form for P (λ).
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Matrix polynomials, Elementary divisors, Inverse problem, Triangularization, Arbitrary fields, Majorization, Homogeneous partitioning
Bibliographic citation
Anguas, L., Dopico, F., Hollister, R., & Mackey, D. (2023). Quasi-triangularization of matrix polynomials over arbitrary fields. Linear Algebra and its Applications, 665, 61-106.