Abstract
A close relationship between the class of totally positive matrices and anti-Monge matrices is used for suggesting a new direction for investigating totally positive matrices. Some questions are posed and a partial answer in the case of Vandermonde-like matrices is given.
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References
S. M. Fallat, C. R. Johnson: Totally Nonnegative Matrices. Princeton Series in Applied Mathematics, Princeton University Press, Princeton, 2011.
M. Fiedler: Subtotally positive and Monge matrices. Linear Algebra Appl. 413 (2006), 177–188.
M. Fiedler: Remarks on Monge matrices. Math. Bohem. 127 (2002), 27–32.
M. Fiedler: Equilibrated anti-Monge matrices. Linear Algebra Appl. 335 (2001), 151–156.
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Supported by Institutional Research Plan of The Czech Academy of Sciences RVO: 67985807, 67985840 and by grant 14-07880S of GA ČR.
Remark from the Editors: This paper was accepted in early summer of 2015, and its galleys were approved by Miroslav Fiedler on October 26 that year, less than a month before his death. Obviously this special issue of CMJ is the right place for this paper. It still fills us with great sadness that its author will not already see it.
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Fiedler, M. A new look at totally positive matrices. Czech Math J 66, 597–602 (2016). https://doi.org/10.1007/s10587-016-0280-z
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DOI: https://doi.org/10.1007/s10587-016-0280-z