Uniqueness of the “nonsingular core” for Hermitian and other matrix pencils |
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Authors: | C S Ballantine E L Yip |
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Institution: |
a Department of Mathematics, Oregon State University, Corvallis, Oregon
b Boeing Computer Services, Inc., Seattle, Washington |
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Abstract: | Every pencil of hermitian matrices is conjunctive with a pencil of the form L ⊕ M, where L (the "minimal-indices" part) has no elementary divisors and M (the "nonsingular core") is a nonsingular pencil. Here it is shown that the conjunctivity type ofM is determined by that of L ⊕ M. The same method of proof applies to many other types of pencils, e.g. to congruence of pencils based on (1) a pair of symmetric matrices, (2) a pair of alternating matrices, or (3) a symmetric and an alternating matrix. |
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