Hermitian positive-definite matrices
On Shift-splitting Based C-to-R Method for Singular Complex Linear Systems
... non-Hermitian positive definite matrices [ 7 ] and by making use of the efficient C- to-R method for nonsingular two-by-two linear system [ 3 ] , we will construct an SS-C-to-R method for ...
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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 ...
9
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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On some trace inequalities for positive definite Hermitian matrices
... a positive definite Hermitian matrix, we investigate the trace inequalities of ...of positive definite Hermitian matrices and some elementary inequalities, we extend some previous works ...
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Gyrovector Spaces on the Open Convex Cone of Positive Definite Matrices
... In this article we review an algebraic definition of the gyrogroup and a simplified version of the gyrovector space with two fundamental examples on the open ball of finite-dimensional Euclidean spaces, which are the ...
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A note on the Frobenius conditional number with positive definite matrices
... given matrices. A matrix A Î ℂ n×n is Hermitian if A H = A. An Hermitian matrix A is said to be positive semidefinite or nonnegative defi- nite, written as A ≥ 0, if (see, ...
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Accelerated normal and skew-Hermitian splitting methods for positive definite linear systems
... the matrices N and S in the above ANSS iteration so that we may first solve the system of linear equations with coefficient matrix βI + S and then solve the system of linear equations with coefficient matrix αI + ...
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Some inequalities for sums of nonnegative definite matrices in quaternions
... two Hermitian matrices A and B of the same order are said to satisfy the L¨owner partial ordering A B if B − A is nonnegative ...is Hermitian positive definite with its eigenvalues λ 1 ...
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Translucent Voices: Creating Sound Pedagogy And Safe Spaces For Transgender Singers In The Choral Rehearsal
... make positive definite matrices so special and interesting to ...is positive definite, and if it is, you suddenly gain a plethora of other properties for that matrix which may have been ...
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On the Minimum of a Positive Definite Quadratic Form over Non--Zero Lattice points. Theory and Applications
... The most basic problem when considering a channel of communication is to determine whether the received information is reliable; that is, to what extent the noise affects the quality of the signal. In order to make the ...
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Some inequalities for generalized eigenvalues of perturbation problems on Hermitian matrices
... Let A, B ∈ C n×n be Hermitian matrices with B being positive definite. We now consider a perturbation problem for Ax = λBx. It is known that the n generalized eigenvalues of the matrix pencil A, B are ...
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Quantum time evolution in terms of nonredundant probabilities
... Furthermore, there is a link to the “probability represen- tation” for both quantum particles and spins [12] which is based on positive smooth distributions on the classi- cal phase space of the underlying system. ...
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Quantum singular-value decomposition of nonsparse low-rank matrices
... nonsparse matrices in an oracular setting that requires only one-sparse simulation ...the matrices are not restricted to be positive semidefinite and the samples required are simple uniform ...
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A General Hermitian Nonnegative Definite Solution to the Matrix Equation AXB = C
... In their efforts to derive a solution, Khatri and Mitra in [12] have employed an innovative technique that converts (9) to an equation in which the coefficient matrices are equal. We call this technique ...
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K hermitian doubly stochastic, s hermitian doubly stochastic and s k hermitian doubly stochastic matrices
... stochastic matrices then A* = V ̅ V and B* = V V To prove A B is s-Hermitian doubly stochastic matrix we will show that AB = = V (A B )* V Now V (A B )* V= V(B*A*)V = V(V V)( V ̅ V)V where A* = V ̅ V and B* ...
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Orthogonal polynomials from Hermitian matrices. II
... As an application of orthogonal polynomials of a discrete variable, here we comment on birth and death processes [4]. A Birth and Death (BD) process is a typical stationary Markov process with a one-dimensional discrete ...
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Motor Imagery Classification Based on Bilinear Sub-Manifold Learning of Symmetric Positive-Definite Matrices
... To obtain a more sophisticated analysis of the 30-fold cross-validation experiment, we calculated the confusion matrix of all studied algorithms corresponding to the results in Table II. A graphical representation of the ...
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Threshold Extension of Gallium Arsenide/Aluminum Gallium Arsenide Terahertz Detectors and Switching in Heterostructures
... certain positive definite programming ...a positive definite matrix which is a real linear combination of some given symmetric matrices A 1 , A 2 , ...
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Generalized Wishart processes for interpolation over diffusion tensor fields
... non- positive definite tensors. Although, non-positive definite tensors are avoided with log-euclidean interpolation, the accuracy of tensor estimation in new input locations is not ...
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Rank modifications of semi-definite matrices with applications to secant updates
... viewpoint, we develop general conditions on how the rank modication should be carried out to maintain the positive semi-deniteness. This development generalizes the class of BFGS and DFP updates both in terms of ...
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