Results 11 to 20 of about 2,874 (210)
Affine Processes on Positive Semidefinite Matrices [PDF]
SSRN Electronic Journal, 2009 This article provides the mathematical foundation for stochastically continuous affine processes on the cone of positive semidefinite symmetric matrices. This analysis has been motivated by a large and growing use of matrix-valued affine processes in finance, including multi-asset option pricing with stochastic volatility and correlation structures ...
Cuchiero, Christa +3 more
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The resolvent average for positive semidefinite matrices [PDF]
Linear Algebra and its Applications, 2010 We define a new average - termed the resolvent average - for positive semidefinite matrices. For positive definite matrices, the resolvent average enjoys self-duality and it interpolates between the harmonic and the arithmetic averages, which it approaches when taking appropriate limits. We compare the resolvent average to the geometric mean.
Bauschke, Heinz H. +2 more
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On the cone of positive semidefinite matrices [PDF]
Linear Algebra and its Applications, 1987 An as yet unsolved problem in matrix theory is to classify those linear transformations of the \(n\times n\) complex matrices which leave the cone, PSD, of positive semidefinite Hermitian matrices invariant. The present note surveys the known results on the structure of the cone PSD, and some of the results concerning linear transformations which map ...
Hill, Richard D., Waters, Steven R.
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Matrices with high completely positive semidefinite rank [PDF]
Linear Algebra and its Applications, 2017 A real symmetric matrix $M$ is completely positive semidefinite if it admits a Gram representation by (Hermitian) positive semidefinite matrices of any size $d$. The smallest such $d$ is called the (complex) completely positive semidefinite rank of $M$, and it is an open question whether there exists an upper bound on this number as a function of the ...
S.J. Gribling (Sander) +2 more
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Products of positive semidefinite matrices [PDF]
Linear Algebra and its Applications, 1988 The author proves that a matrix T is the product of finitely many nonnegative matrices if and only if det(T)\(\geq 0\) and in this case, five such matrices are sufficient.
Wu, Pei Yuan
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Monotonicity of Positive Semidefinite Hermitian Matrices [PDF]
Proceedings of the American Mathematical Society, 1972 Inequalities which compare elements of the convex cone of positive semidefinite hermitian matrices with products of roots of elements are proved. They yield inequalities for Schur functions (generalized matrix functions) which, when specialized to the determinant, give a result of R. Bellman and L. Mirsky.
Merris, R., Pierce, Stephen
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On a product of positive semidefinite matrices [PDF]
Linear Algebra and its Applications, 1999 The matrix \(A\) is said to be positive semidefinite (psd) if there exists a matrix \(P\) such that \(PP^*=A\). If \(A\) and its conjugate transpose \(A^*\) have the same range space, then \(A\) is called EP. Necessary and sufficient conditions are given for the product of two positive semidefinite (psd) matrices to be EP. As a consequence, it is shown
Meenakshi, A.R., Rajian, C.
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On permanents of positive semidefinite matrices [PDF]
Linear Algebra and its Applications, 1985 Let A and B be positive semidefinite real symmetric matrices. Using properties of tensor products, \textit{T. Ando} [Hokkaido Math. J. 10, Special Issue, 10, No.1, 18-36 (1981; Zbl 0484.15006)] proved that \(per(A+B)\geq per A+per B\). In this paper, it is shown that the Binet- Cauchy formula for the permanent of a product of matrices can also be used ...
Bapat, Ravindra, Ravindra Bapat
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TRACE INEQUALITIES OF POSITIVE SEMIDEFINITE MATRICES [PDF]
, 2006 In this paper, the trace inequalities involving special products of the positive semidefinite matrices are investigated. The trace inequalities between the Kronecker product and Kronecker sum of two matrices is obtained as in the short note Yang’s inequalities.
ÖZEL, Mustafa +3 more
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Ergodicity of affine processes on the cone of symmetric positive semidefinite matrices [PDF]
, 2020 This article investigates the long-time behavior of conservative affine processes on the cone of symmetric positive semidefinite d × d matrices. In particular, for conservative and subcritical affine processes we show that a finite log-moment of the ...
Jonas Kremer +7 more
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