A proof of the Tn conjecture: Centralizers,Jacobians and spectrally arbitrary sign patterns |
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Authors: | Colin Garnett Bryan L Shader |
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Institution: | Department of Mathematics, University of Wyoming, 1000 E. University Avenue, Laramie, WY 82071, USA |
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Abstract: | We prove the so-called conjecture: for every real-monic polynomial of degree there exists an n by n matrix with sign patternwhose characteristic polynomial is . The proof converts the problem of determining the nonsingularity of a certain Jacobi matrix to the problem of proving the non-existence of a nonzero matrix B that commutes with a nilpotent matrix with sign pattern and has zeros in positions , and for . |
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