# Factorizing a Matrix Quadratic Polynomial

### From NZJM

[edit]

**New Zealand Journal of Mathematics**

**Vol.** 43, (2013), **Pages** 1-6

**Christopher S. Withers**

Applied Mathematics Group

Industrial Research Limited

Lower Hutt,

New Zealand

**Saralees Nadarajah**

School of Mathematics

University of Manchester

Manchester M13 9PL,

United Kingdom

mailto:Saralees.Nadarajah@manchester.ac.uk

**Abstract** Let *A*_{1}, *A*_{2} lie in and *t* in .
For the matrix quadratic polynomial,
we give explicit solutions for (α_{1},α_{2}) in .
We consider two cases: i) *A*_{1} and *A*_{2} commute;
ii) *A*_{1} and *A*_{2} do not commute.

**Keywords** Factorization; Jordan blocks; Matrix quadratic equation.

**Classification** (MSC2000) 15B99.

[edit]