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The generalized Cayley-Hamilton theorem for standard pencils

1992; Elsevier BV; Volume: 18; Issue: 3 Linguagem: Inglês

10.1016/0167-6911(92)90003-b

ISSN

1872-7956

Autores

F.-R. Chang, H. C. Chen,

Tópico(s)

Magnetism in coordination complexes

Resumo

The Cayley-Hamilton theorem is extended from the case of one matrix to that of two matrices. The developed theorem is suitable for the standard form pencil sE − A. Let Δ(s) := det(sE − A) = Σr=0narsr. Then we show that Σr=0narArEn−r = 0. Such a neat result, which is very similar to the original theorem also, is due to some nice properties of the standard pair {E, A}. For example, E and A commute and share the same eigenspaces.

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