Positive Definite Matrices
Spatial Modeling of Positive Definite Matrices and Its Applications to Diffusion Tensor Imaging.
... to positive definite matrix-variate ...the positive definite matrices follow Wishart distributions and use spatially continuous random fields supporting spatially dependent Wishart ...
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Gyrovector Spaces on the Open Convex Cone of Positive Definite Matrices
... Remark 4.2. It is known in [1, Chapter 6] that ( P , δ) is a Bruhat-Tits space (a Hadamard space or a non-positive curvature space), which is a complete metric space satisfying the semi-parallelogram law. For an ...
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A note on the Frobenius conditional number with positive definite matrices
... is positive definite, then any eigenvalue of A is positive real ...all positive real ...are positive real ...both positive definite. It is obvious that M -1 and N -1 are ...
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Sum of squared logarithms an inequality relating positive definite matrices and their matrix logarithm
... We will proceed as follows: In the first section, we will give several equivalent formulations of the inequality, for example, in terms of the coefficients of the characteristic polynomial [r] ...
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On The Frobenius Condition Number of Positive Definite Matrices
... a positive definite matrix depending on trace, determinant, and Frobenius norm of a positive definite matrix and compare these results with other ...
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Generalized Wishart processes for interpolation over diffusion tensor fields
... symmetric positive definite random matrices indexed by an arbitrary dependent variable [15], ...advantages: positive definite matrices, robustness to noise, smooth transition ...
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Translucent Voices: Creating Sound Pedagogy And Safe Spaces For Transgender Singers In The Choral Rehearsal
... of positive definite matrices, which gives some motivation for our search into the theory of positive definite matrices in finite fields despite the definition’s loss of ...
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Computing the Matrix Geometric Mean of Two HPD Matrices: A Stable Iterative Method
... In this paper, a new iteration scheme for computing the sign of a matrix which has no pure imaginary eigenvalues is presented. Then, by applying a well-known identity in matrix functions theory, an algorithm for ...
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On the Minimum of a Positive Definite Quadratic Form over Non--Zero Lattice points. Theory and Applications
... of positive definite matrices is the so–called Wishart ...random matrices, multidimensional bayesian analysis and more generally in statistics, where its importance stems from the fact that it ...
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On p and q Horn’s Matrix Function of Two Complex Variables
... Many special functions encountered in mathematical physics, theoretical physics, engineering and probability theory are special cases of hypergeometric functions [1]. Hypergeometric series in one and more variables occur ...
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Restricted Algebras on Inverse Semigroups—Part II: Positive Definite Functions
... and positive definite functions is a key concept in harmonic analysis on topological ...restricted positive definite functions and their relation with restricted representations of an inverse ...
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GENERALIZED POSITIVE DEFINITE FUNCTIONS AND COMPLETELY MONOTONE FUNCTIONS ON FOUNDATION SEMIGROUPS
... all positive multiplicative linear functionals on ...to positive A-valued measures on , the space of all w-bounded continuous nonnegative semicharac- ters on a foundation semigroup S with a Borel measurable ...
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Matrices whose hermitian part is positive definite
... OF HADAMARD'S INEQUALITY The inequality of Hadamard [24] holds for a matrix in MnC when the absolute value of its determinant is dominated ~ by the absolute value of the product of its [r] ...
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Low Rank Positive Approximants of Symmetric Matrices
... low-rank positive approximant of X. That is, a symmetric positive semidefinite matrix, S, whose rank is smaller than a given posi- tive integer, , which is nearest to X in a certain matrix ...
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Universality, Characteristic Kernels and RKHS Embedding of Measures
... of positive definite (pd) kernels—universal and characteristic—have been developing in parallel in machine learning: universal kernels are pro- posed in the context of achieving the Bayes risk by ...
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Causes and effects of negative definite covariance matrices in Swamy Type Random Coefficient Models
... Given that ˆ 4, described in equation (8), is a plug-in estimator, we also test whether the finite sample performances (in terms of bias and RMSE) of both the Mean Group estimator of c and β, and the OLS estimators of ...
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Kernel Bayes' Rule: Bayesian Inference with Positive Definite Kernels
... kernel means of the underlying random variables. With an appropriate choice of positive definite kernel, the kernel mean on the RKHS uniquely determines the distribution of the variable (Fukumizu et al., ...
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Vol 3, No 5 (2012)
... nonsingular matrices A, B, if A ≥ B ≥ 0, then B -1 ≥ A -1 ≥ ...singular matrices A ≥ B ≥ 0 by Hans ...a.p.d matrices. For a pair of Complex a.p.d matrices A and B such that A ≥ B, conditions ...
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On Positive Definite Solutions of Nonlinear Matrix Equation X A*X( 1)A = I
... which is generated randomly by the MATLAB function (2 ∗ rand(4) − 1) + i ∗ (2 ∗ rand(4) − 1). We compute the unique positive definite solution X of equation (3) by fixed-point iteration (5) and the ...
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Accelerated normal and skew-Hermitian splitting methods for positive definite linear systems
... normal matrices. Therefore, the linear systems with the coefficient matrices αI + N and βI + S may be solved accurately and efficiently by some Krylov subspace iteration methods, ...
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