Results 1 to 10 of about 10,153 (131)
Totally Positive Wronskian Matrices and Symmetric Functions
AxiomsThe elements of the bidiagonal decomposition (BD) of a totally positive (TP) collocation matrix can be expressed in terms of symmetric functions of the nodes. Making use of this result, and studying the relation between Wronskian and collocation matrices
Pablo Díaz +2 more
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On totally positive matrices and geometric incidences
Journal of Combinatorial Theory - Series A, 2014 11 ...
Miriam Farber +2 more
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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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Sums of totally positive matrices
Linear Algebra and Its Applications, 2004 An \(m\times n\) matrix is called totally positive if all of its minors are positive. The authors prove that an arbitrary \(m\times n\) positive matrix can be written as a sum of at most \(\min\{m, n\}\) totally positive matrices. This generalizes the fact that a positive matrix is the sum of two matrices whose all principal minors are positive.
D D Olesky
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Linear Algebra and Its Applications, 1987 As a survey paper on totally positive matrices, this article enhances the earlier work of Gantmacher and Krein, and Karlin. There are seven short sections, each complete with definitions, theorems, proofs and references on: determinantal identities in light of tensor products and Schur complements; criteria for total positivity using sign-regularity ...
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M-matrices whose inverses are totally positive
Linear Algebra and Its Applications, 1995 A real invertible \(n \times n\) matrix with nonpositive off-diagonal elements is an \(M\)-matrix provided \(Ax \geq 0\) implies \(x \geq 0\) for all \(x \in {\mathcal F}^n\). The author shows that if \(A\) is such a matrix, then \(A^{- 1}\) is totally positive (i.e., all minors are nonnegative) if and only if \(A\) is a tridiagonal matrix.
J M Pena
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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.
E. Salinelli, SGARRA, CARLO
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On the Total Positivity and Accurate Computations of r-Bell Polynomial Bases
Axioms, 2023 A new class of matrices defined in terms of r-Stirling numbers is introduced. These r-Stirling matrices are totally positive and determine the linear transformation between monomial and r-Bell polynomial bases.
Esmeralda Mainar +2 more
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