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Algebra |
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Authors: Yaroslav Shitov
A sign pattern is a matrix with entries in {+, −, 0}. An n × n sign pattern S is spectrally arbitrary if, for any monic polynomial f of degree n with real coefficients, one can replace the + and − signs in S with real numbers of the corresponding signs so that the resulting matrix has characteristic polynomial f. This paper refutes a long-standing conjecture with a construction of an n × n spectrally arbitrary sign pattern with less than 2n entries nonzero.
Comments: 21 Pages.
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[v1] 2020-12-08 20:02:04
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