Results 81 to 90 of about 41,274 (203)
Moore-Penrose inverse of a hollow symmetric matrix and a predistance matrix
Special Matrices, 2016 By a hollow symmetric matrix we mean a symmetric matrix with zero diagonal elements. The notion contains those of predistance matrix and Euclidean distance matrix as its special cases.
Kurata Hiroshi, Bapat Ravindra B.
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Spatial Image Gradient Estimation From the Diffusion MRI Profile
Magnetic Resonance in Medicine, Volume 95, Issue 5, Page 2980-2991, May 2026.ABSTRACT Purpose In the course of diffusion, water molecules encounter varying values for the relaxation‐time properties of the underlying tissue. This factor, which has rarely been accounted for in diffusion MRI (dMRI), is modeled in this work, allowing for the estimation of the gradient of relaxation‐time properties from the dMRI signal. Methods With
Iman Aganj +4 more
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Log-Determinant Divergences Revisited: Alpha-Beta and Gamma Log-Det Divergences
Entropy, 2015 This work reviews and extends a family of log-determinant (log-det) divergences for symmetric positive definite (SPD) matrices and discusses their fundamental properties.
Andrzej Cichocki +2 more
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On directional derivatives of trace functionals of the form $A\mapsto\Tr(Pf(A))$
, 2018 Given a function $f:(0,\infty)\rightarrow\RR$ and a positive semidefinite $n\times n$ matrix $P$, one may define a trace functional on positive definite $n\times n$ matrices as $A\mapsto \Tr(Pf(A))$.
Girard, Mark W.
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Extremal positive semidefinite doubly stochastic matrices
Linear Algebra and its Applications, 1991 This paper continues the investigation initiated by \textit{J. P. R. Christensen} and \textit{P. Fischer} [ibid. 82, 123-132 (1986; Zbl 0599.15011)] on the extreme points of \(K_ n=H_ n\cap \Omega_ n\), the intersection set of the closed convex cone \(H_ n\) of all real \(n\times n\) symmetric positive semidefinite matrices and the compact convex set \(
Grone, Bob, Pierce, Steve
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Entrywise transforms preserving matrix positivity and nonpositivity
Journal of the London Mathematical Society, Volume 113, Issue 5, May 2026.Abstract We characterize real and complex functions which, when applied entrywise to square matrices, yield a positive definite matrix if and only if the original matrix is positive definite. We refer to these transformations as sign preservers. Compared to the classical work on entrywise preservers by Schoenberg and others, we completely resolve this ...
Dominique Guillot +3 more
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A Geometric Mean of Parameterized Arithmetic and Harmonic Means of Convex Functions
Abstract and Applied Analysis, 2012 The notion of the geometric mean of two positive reals is extended by Ando (1978) to the case of positive semidefinite matrices A and B. Moreover, an interesting generalization of the geometric mean A # B of A and B to convex functions was introduced by ...
Sangho Kum, Yongdo Lim
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Rank inequalities for positive semidefinite matrices
Linear Algebra and its Applications, 1996 Several inequalities relating the rank of a positive semidefinite matrix with the ranks of various principal submatrices are presented. These inequalities are analogous to known determinantal inequalities for positive definite matrices, such as Fischer's inequality, Koteljanskii's inequality, and extensions of these associated with chordal graphs.
Lundquist, Michael, Barrett, Wayne
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ON THE SET-SEMIDEFINITE REPRESENTATION OF NONCONVEX QUADRATIC PROGRAMS WITH CONE CONSTRAINTS
Croatian Operational Research Review, 2010 The well-known result stating that any non-convex quadratic problem over the non-negative orthant with some additional linear and binary constraints can be rewritten as linear problem over the cone of completely positive matrices (Burer, 2009) is ...
Gabriele Eichfelder, Janez Povh
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The geometry of low-rank Kalman filters [PDF]
, 2013 An important property of the Kalman filter is that the underlying Riccati flow is a contraction for the natural metric of the cone of symmetric positive definite matrices. The present paper studies the geometry of a low-rank version of the Kalman filter.
Bonnabel, Silvere, Sepulchre, Rodolphe
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