Smith Forms of Palindromic Matrix Polynomials
By D. Steven Mackey, Niloufer Mackey, Christian Mehl, Volker Mehrmann. 2011
55 citations recorded by the source corpus.
Many applications give rise to matrix polynomials whose coefficients have a kind of reversal symmetry, a structure we call palindromic. Several properties of scalar palindromic polynomials are derived, and together with properties of compound matrices, used to establish the Smith form of regular and singular $T$-palindromic matrix polynomials over arbitrary fields. The invariant polynomials are shown to inherit palindromicity, and their structure is described in detail. Jordan structures of palindromic matrix polynomials are characterized, and necessary conditions for the existence of structured linearizations established. In the odd degree case, a constructive procedure for building palindromic linearizations shows that the necessary conditions are sufficient as well. The Smith form for $*$-palindromic polynomials is also analyzed. Finally, results for palindromic matrix polynomials over fields of characteristic two are presented.
Subfields: Computational Theory and Mathematics, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/0bf43597447acfaaf1200dd85f3f6229ec2db20b
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In Computational Theory and Mathematics
- Froilán M. Dopico
- Fernando De Terán
- D. Steven Mackey
- Valeria Simoncini
- Volker Mehrmann
- An M. Dopico
- Fernando De Ter
In Numerical Analysis
Citations in the corpus
- Spectral equivalence of matrix polynomials and the index sum theorem (2014, methodology): “However, this research has also shown that in certain important classes of structured matrix polynomials there always exist polynomials P (λ) of even degree which do not have any linearization in the same structure class [41, 42, 43].”