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- W2066248820 abstract "Two main results are established. Stated imprecisely, the first asserts that if a selfadjoint matrix polynomial L(λ) has enough eigenvectors of positive type then they contain a complete set, and hence L(λ) has a right-divisor of the form λI − Z. (A similar result holds for eigenvectors of negative type.) For this result the leading coefficient A of L(λ) may be singular and/or indefinite. The second result is established under the conditions that L(λ) has even degree, A is nonsingular, and all eigenvalues of L(λ) are real with only linear elementary divisors. It is shown that, in this case, there is a factorization L(λ) = M ∗{λ)N{λ) with monic polynomials M(λ)N(λ) determined by the eigenvectors of L(λ) of positive and negative types, respectively. It is shown that there is no analogous result when L(λ) has odd degree." @default.
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- W2066248820 date "1996-01-01" @default.
- W2066248820 modified "2023-09-26" @default.
- W2066248820 title "Factorization of selfadjoint matrix polynomials with reas Spectrum" @default.
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- W2066248820 doi "https://doi.org/10.1080/03081089608818449" @default.
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