You are here: MIMS > EPrints
MIMS EPrints

## 2012.77: Triangularization of matrix polynomials

2012.77: Leo Taslaman, Francoise Tisseur and Ion Zaballa (2012) Triangularization of matrix polynomials.

Full text available as:

 PDF - Archive staff only - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader341 Kb

## Abstract

For an algebraically closed field $\F$, we show that any matrix polynomial $P(\l)=\sum_{j=0}^\ell \l^jA_j$ with $A_j\in\F^{\nbym}$, $n\le m$, can be reduced over $\F[\l]$ to an $\nbym$ upper triangular matrix polynomial of grade $\ell$ preserving the finite and infinite elementary divisors. We also characterize the real matrix polynomials that are triangularizable over the real numbers and show that those that are not triangularizable are quasi-triangularizable with diagonal blocks of sizes $1\times 1$ and $2\times 2$.

Item Type: MIMS Preprint MSC 2000 > 15 Linear and multilinear algebra; matrix theoryMSC 2000 > 65 Numerical analysis 2012.77 Dr Françoise Tisseur 09 August 2012