Factorizing a Matrix Quadratic Polynomial


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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


Abstract Let A1, A2 lie in {\mathbb{C}}^{r\times r} and t in {\mathbb{C}}. For the matrix quadratic polynomial, I+A_1t+A_2t^2 = \left( I - \alpha_1t \right) \left(I - \alpha_2t \right), we give explicit solutions for 12) in {\mathbb{C}}^{r\times r}. We consider two cases: i) A1 and A2 commute; ii) A1 and A2 do not commute.

Keywords Factorization; Jordan blocks; Matrix quadratic equation.

Classification (MSC2000) 15B99.

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