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Positive Hankel Matrices, Eigenvalues and Total Positivity
MathematicsFor positive Hankel matrices, an interval containing all eigenvalues is obtained. With a stronger condition, we also construct two sharper intervals for the eigenvalue localization. The total positivity of positive Hankel matrices is analyzed.
Juan Manuel Peña
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Permanental Inequalities for Totally Positive Matrices
The Electronic Journal of CombinatoricsWe characterize ratios of permanents of (generalized) submatrices which are bounded on the set of all totally positive matrices. This provides a permanental analog of results of Fallat, Gekhtman, and Johnson [Adv. Appl. Math. 30 (2003), 442-470] concerning ratios of matrix minors. We also extend work of Drake, Gerrish, and the first author [Electron. J.
Mark A. Skandera, Daniel Soskin
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Inner totally positive matrices [PDF]
Linear Algebra and its Applications, 2004 The author considers the concept of inner total positivity. In Section 1, he describes the notation and basic theory used in this paper, concerning totally positivity and nonnegativity. In Section 2, he generalizes the results in Section 1 to inner totally positive (totally nonnegative) matrices.
Gladwell, G.M.L.
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Parametrizations of Canonical Bases and Totally Positive Matrices
Advances in Mathematics, 1996 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Sergey Fomin +2 more
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Totally Positive Density Matrices and Linear Preservers [PDF]
The Electronic Journal of Linear Algebra, 2016 The intersection between the set of totally nonnegative matrices, which are of interest in many areas of matrix theory and its applications, and the set of density matrices, which provide the mathematical description of quantum states, are investigated.
Kribs, David W. +2 more
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Totally positive matrices and cyclic polytopes [PDF]
Linear Algebra and its Applications, 1988 As the main result of the present note it is proved that there is a natural correspondence between alternating polytopes and totally positive matrices. A real (n-d)\(\times d\) matrix A, where \(n>d>1\) is totally positive (totally nonnegative) if all subdeterminants of A are positive (nonnegative).
Sturmfels, Bernd, Sturmfels, B.
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Possible spectra of totally positive matrices [PDF]
Linear Algebra and its Applications, 1984 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Barrett, Wayne W., Johnson, Charles R.
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The Stability Analysis of Linear Systems with Cauchy—Polynomial-Vandermonde Matrices
Axioms, 2023 The numerical approximation of both eigenvalues and singular values corresponding to a class of totally positive Bernstein–Vandermonde matrices, Bernstein–Bezoutian structured matrices, Cauchy—polynomial-Vandermonde structured matrices, and quasi ...
Mutti-Ur Rehman +3 more
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Total positivity of Narayana matrices [PDF]
Discrete Mathematics, 2018 We prove the total positivity of the Narayana triangles of type $A$ and type $B$, and thus affirmatively confirm a conjecture of Chen, Liang and Wang and a conjecture of Pan and Zeng. We also prove the strict total positivity of the Narayana squares of type $A$ and type $B$.
Yi Wang 0027, Arthur L. B. Yang
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Correlation matrices of yields and total positivity [PDF]
Linear Algebra and its Applications, 2006 Using some tools originally developed in the framework of totally positive matrices, the relations between the spectral properties of the correlation matrices of forward interest rates and the positivity and the monotonicity of their elements are investigated.
SALINELLI, Ernesto, C. Sgarra
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