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A weak property L for pairs of matrices

Taussky, Olga (1959) A weak property L for pairs of matrices. Mathematische Zeitschrift, 71 (1). pp. 463-465. ISSN 0025-5874. doi:10.1007/bf01181419. https://resolver.caltech.edu/CaltechAUTHORS:20201022-100905183

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Abstract

A pair of n x n matrices A, B with complex numbers as elements is said to have the L-property if λA + µB has as characteristic roots λα_i + µβ_i, where α_i are the characteristic roots of A and β_i the characteristic roots of B--taken in a special ordering--and when λ,µ run through all complex numbers. Let one of the matrices, say A, be diagonable (i.e. similar to a diagonal matrix). The following condition on B is then necessary for A and B to have property L (see T. S. MOTZKIN and O. TAUSSKY [1] p. 108--109).


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https://doi.org/10.1007/bf01181419DOIArticle
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Additional Information:© 1959 Springer. (Eingegangen am 18, März 1959)
Issue or Number:1
DOI:10.1007/bf01181419
Record Number:CaltechAUTHORS:20201022-100905183
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20201022-100905183
Official Citation:Taussky, O. A weak property L for pairs of matrices. Math Z 71, 463–465 (1959). https://doi.org/10.1007/BF01181419
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:106214
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:22 Oct 2020 22:45
Last Modified:16 Nov 2021 18:51

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