Subtotally positive and Monge matrices |
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Authors: | Miroslav Fiedler |
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Institution: | Institute of Computer Science, Czech Academy of Sciences, Pod vodárenskou vě?í 2, 18207 Praha 8, Czech Republic |
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Abstract: | A real matrix is called k-subtotally positive if the determinants of all its submatrices of order at most k are positive. We show that for an m × n matrix, only mn inequalities determine such class for every k, 1 ? k ? min(m,n). Spectral properties of square k-subtotally positive matrices are studied. Finally, completion problems for 2-subtotally positive matrices and their additive counterpart, the anti-Monge matrices, are investigated. Since totally positive matrices are 2-subtotally positive as well, the presented necessary conditions for this completion problem are also necessary conditions for totally positive matrices. |
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Keywords: | 15A57 15A48 |
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