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Invariant subspace, determinant and characteristic polynomials

✍ Scribed by Yaokun Wu

Publisher: Elsevier Science
Year: 2008
Tongue: English
Weight: 124 KB
Volume: 428
Category: Article
ISSN: 0024-3795
DOI: 10.1016/j.laa.2007.10.014

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✦ Synopsis

Making use of an elementary fact on invariant subspace and determinant of a linear map and the method of algebraic identities, we obtain a factorization formula for a general characteristic polynomial of a matrix. This answers a question posed in [A. Deng, I. Sato, Y. Wu, Characteristic polynomials of ramified uniform covering digraphs, European J. Combin. 28 (2007Combin. 28 ( ) 1099Combin. 28 ( -1114]]. The approach of this work can be used to supply alternative proofs of several other earlier results, including some results of [Y. Teranishi, Equitable switching and spectra of graphs, Linear Algebra Appl. 359 (2003) 121-131].

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