Hermitian pencils with a cubic minimal polynomial |
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Authors: | Helene Shapiro |
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Institution: | Department of Mathematics Swarthmore College Swarthmore, Pennsylvania 19081USA |
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Abstract: | Let A be an n × n complex matrix and write A = H + iK, where H and K are Hermitian matrices. We show that if the minimal polynomial of the pencil xH + yK has degree 3, then there is a unitary matrix U such that U-1AU is block diagonal with blocks of size 3 × 3 or smaller. This is a special case of a conjecture made by Kippenhahn in 1951. |
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