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Article

Keywords:
totally positive matrix; Monge matrix; semigroup; Vandermonde-like matrix
Summary:
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.
References:
[1] Fallat, S. M., Johnson, C. R.: Totally Nonnegative Matrices. Princeton Series in Applied Mathematics Princeton University Press, Princeton (2011). MR 2791531
[2] Fiedler, M.: Subtotally positive and Monge matrices. Linear Algebra Appl. 413 (2006), 177-188. DOI 10.1016/j.laa.2005.08.020 | MR 2202101 | Zbl 1090.15016
[3] Fiedler, M.: Remarks on Monge matrices. Math. Bohem. 127 (2002), 27-32. MR 1895243 | Zbl 1003.15022
[4] Fiedler, M.: Equilibrated anti-Monge matrices. Linear Algebra Appl. 335 (2001), 151-156. MR 1850820 | Zbl 0983.15023
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