Results 41 to 50 of about 294,893 (309)

Ergodic Decomposition for Inverse Wishart Measures on Infinite Positive-Definite Matrices [PDF]

Symmetry, Integrability and Geometry: Methods and Applications, 2019
The ergodic unitarily invariant measures on the space of infinite Hermitian matrices have been classified by Pickrell and Olshanski-Vershik. The much-studied complex inverse Wishart measures form a projective family, thus giving rise to a unitarily ...
T. Assiotis
semanticscholar   +1 more source

Positive Definite Norm Dependent Matrices In Stochastic Modeling

Demonstratio Mathematica, 2014
Positive definite norm dependent matrices are of interest in stochastic modeling of distance/norm dependent phenomena in nature. An example is the application of geostatistics in geographic information systems or mathematical analysis of varied spatial ...
Kuniewski Sebastian P., Misiewicz Jolanta K.   +1 more
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A New Slack Lyapunov Functional for Dynamical System with Time Delay

Mathematics, 2022
The traditional method of constructing a Lyapunov functional for dynamical systems with time delay is usually dependent on positive definite matrices in the quadratic form.
Can Zhao, Kaibo Shi, Yiqian Tang, Shouming Zhong   +3 more
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Inequalities for the Wasserstein mean of positive definite matrices [PDF]

Linear Algebra and its Applications, 2018
We prove majorization inequalities for different means of positive definite matrices. These include the Cartan mean (the Karcher mean), the log Euclidean mean, the Wasserstein mean and the power mean.
R. Bhatia, Tanvi Jain, Y. Lim
semanticscholar   +1 more source

Determinant Inequalities for Positive Definite Matrices Via Additive and Multiplicative Young Inequalities

Revista Integración, 2022
In this paper we prove among others that, if the positive definite matrices A, B of order n satisfy the condition 0 < mIn ≤ B − A ≤ M In, for some constants 0 < m < M, where In is the identity matrix, then0 ≤ (1 − t) [det (A)]−1 + t [det (A + mIn)]−1 − [
Silvestru Sever Dragomir
doaj  

NEW PROPOSED METHODS FOR CODING INFORMATION USING DIRECT PRODUCT OF SYMMETRIC MATRICES AND CONTRACTION FUNCTIONS WITH NEW PROPERTIES OF HERMITIAN MATRICES

Journal of Kufa for Mathematics and Computer, 2010
In this paper, two separately methods were suggested for coding information .The first method was introduced using the directness of symmetric matrices .The contraction function was used for introducing the second method .For more complexity the ...
Adel Mohammad Hassan Rizak Al-Rammahi
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Determinant Inequalities for Positive Definite Matrices Via Diananda’s Result for Arithmetic and Geometric Weighted Means

Annals of the West University of Timisoara: Mathematics and Computer Science, 2023
In this paper we prove among others that, if (Aj)j=1,...,m are positive definite matrices of order n ≥ 2 and qj ≥ 0, j = 1, ..., m with ∑j=1mqj=1$$\sum\nolimits_{j = 1}^m {{q_j} = 1} $$, then 0≤11−mini∈{1,…,m}{qi}×[∑​i=1mqi(1−qi)[det(Ai)]−1−2n+1∑​1 ...
Dragomir Silvestru Sever
doaj   +1 more source

Positive Definite Matrices and Catalan Numbers [PDF]

Proceedings of the American Mathematical Society, 1980
It is shown that the number of n × n n \times n integral triple diagonal matrices which are unimodular, positive definite and whose sub and super diagonal elements are all one, is the Catalan number ( n 2 n ) /
Leighton, Frank Thomson, Newman, Morris
openaire   +2 more sources

Geometric Distance Between Positive Definite Matrices of Different Dimensions [PDF]

IEEE Transactions on Information Theory, 2018
We show how the geodesic distance on $\mathbb {S}^{n}_{+ + }$ , the cone of $n\times n$ real symmetric or complex Hermitian positive definite matrices regarded as a Riemannian manifold, may be used to naturally define a distance between two such ...
Lek-Heng Lim, R. Sepulchre, Ke Ye
semanticscholar   +1 more source

Dimensionality Reduction of SPD Data Based on Riemannian Manifold Tangent Spaces and Isometry

Entropy, 2021
Symmetric positive definite (SPD) data have become a hot topic in machine learning. Instead of a linear Euclidean space, SPD data generally lie on a nonlinear Riemannian manifold.
Wenxu Gao, Zhengming Ma, Weichao Gan, Shuyu Liu   +3 more
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