## 2012.77: Triangularization of matrix polynomials

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

There is a more recent version of this eprint available. Click here to view it.

Full text available as:

PDF - Archive staff only - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader 341 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 |
---|---|

Subjects: | MSC 2000 > 15 Linear and multilinear algebra; matrix theory MSC 2000 > 65 Numerical analysis |

MIMS number: | 2012.77 |

Deposited By: | Dr Françoise Tisseur |

Deposited On: | 09 August 2012 |

### Available Versions of this Item

- Triangularizing matrix polynomials (deposited 02 November 2012)
- Triangularization of matrix polynomials (deposited 09 August 2012)
**[Currently Displayed]**

- Triangularization of matrix polynomials (deposited 09 August 2012)

Download Statistics: last 4 weeks

Repository Staff Only: edit this item