Linearization of regular matrix polynomials

By Peter Lancaster. 2008

54 citations recorded by the source corpus.

This note contains a short review of the notion of linearization of regular matrix polynomials. The objective is clarification of this notion when the polynomial has an "eigenvalue at infinity". The theory is extended to admit reduction by locally unimodular analytic matrix functions.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/34ef31b37640096062241102380c0f0178ae7707

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. D. Steven Mackey
2. Volker Mehrmann
3. Christian Mehl
4. Niloufer Mackey

In Computational Theory and Mathematics

1. D. Steven Mackey
2. Volker Mehrmann
3. Christian Mehl
4. Niloufer Mackey
5. Peter Lancaster
6. Robert M Corless
7. Amirhossein Amiraslani
8. Fernando De Terán

In Geometry and Topology

1. D. Steven Mackey
2. Volker Mehrmann
3. Christian Mehl
4. Niloufer Mackey

Citations in the corpus

• Linearization of matrix polynomials expressed in polynomial bases (2008, background): “By Theorem A.3.4 of [14] P ](λ) = E0(λ) diag [ λm1 , · · · , λmt , 1, · · · , 1 ] F0(λ) (44) for matrix polynomials E0(λ), F0(λ) invertible at 0 and since P ](0) = An, it follows that n− t = rank(An), or t = n− rank(An).”
• Möbius transformations of matrix polynomials (2015, background): “9 can be relaxed as in [40] to allow Eλ0(λ) and Fλ0(λ) to be any matrix functions that are invertible at λ0 and analytic in a neighborhood of λ0 (e.”
• Smith Forms of Palindromic Matrix Polynomials (2011, unknown): “(This notion was considered by Gohberg, Kaashoek and Lancaster in [8], and called “extended degree” in [16].”