Complex eigenvalues of a non-negative matrix with a specified graph |
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| Authors: | RB Kellogg AB Stephens |
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| Institution: | Institute for Fluid Dynamics and Applied Mathematics University of Maryland College Park, Maryland 20742, U.S.A.;Department of Science and Mathematics Mount St. Mary''s College Emmitsburg, Maryland 21727, U.S.A. |
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| Abstract: | Let A be a non-negative matrix of order n with Perron eigenvalue ? and associated directed graph G. Let m be the length of the longest circuit of G. Theorem: If m=2, all eigenvalues of A are real. If 2<m?n, and if λ=μ+iv is an eigenvalue of A, then . |
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