A note on maximizing the permanent of a positive definite hermitian matrix, given the eigenvalues |
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| Authors: | Robert Grone Charles R Johnson SA Eduardo Henry Wolkowicz |
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| Institution: |
a Department of Mathematics, Auburn University, Auburn, Alabama
b Mathematical Sciences Department, Clemson University, Clemson, South Carolina
c Departamento de Matematica, Universidade de Coimbra, Coimbra, Portugal
d Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada |
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| Abstract: | As a step toward understanding the unsolved problem of determining how large the permanent of a positive semi-definite matrix can be, given the eigenvalues, we note that a necessary condition for A to be a permanent maximizing matrix is that A commute with its permanental adjoint. |
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