Results 1 to 10 of about 2,871 (211)
Fall Detection of Elderly People Using the Manifold of Positive Semidefinite Matrices [PDF]
Journal of Imaging, 2021 Falls are one of the most critical health care risks for elderly people, being, in some adverse circumstances, an indirect cause of death. Furthermore, demographic forecasts for the future show a growing elderly population worldwide.
Abdessamad Youssfi Alaoui +5 more
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Trace inequalities for positive semidefinite matrices
Discussiones Mathematicae - General Algebra and Applications, 2017 Certain trace inequalities for positive definite matrices are generalized for positive semidefinite matrices using the notion of the group generalized inverse.
Choudhury Projesh Nath, Sivakumar K.C.
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Functions Operating on Positive Semidefinite Quaternionic Matrices
Monatshefte Fur Mathematik, 2001 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Helge Glöckner
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Singular Values of Differences of Positive Semidefinite Matrices [PDF]
SIAM Journal on Matrix Analysis and Applications, 2001 Based on known results, the author shows relations between the singular values of two positive semidefinite matrices. Let \(A\) and \(B\) be complex positive semidefinite matrices of order \(n\) and let us denote as \(A \oplus B\) the block diagonal matrix with \(A\) and \(B\) on the diagonal. Using the common notation for singular values \(s_1(.) \geq
Xingzhi Zhan
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The resolvent average for positive semidefinite matrices
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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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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A trace bound for integer-diagonal positive semidefinite matrices
Special Matrices, 2020 We prove that an n-by-n complex positive semidefinite matrix of rank r whose graph is connected, whose diagonal entries are integers, and whose non-zero off-diagonal entries have modulus at least one, has trace at least n + r − 1.
Mitchell Lon
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On the cone of positive semidefinite matrices
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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On Positive Semidefinite Matrices with Known Null Space [PDF]
SIAM Journal on Matrix Analysis and Applications, 2002 We show how the zero structure of a basis of the null space of a positive semidefinite matrix can be exploited to determine a positive definite submatrix of maximal rank. We discuss consequences of this result for the solution of (constrained) linear systems and eigenvalue problems.
Peter Arbenz, Zlatko Drmač
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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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