Results 31 to 40 of about 5,394,718 (279)

Some trace inequalities for matrix means

Journal of Inequalities and Applications, 2016
In this short note, we present some trace inequalities for matrix means. Our results are generalizations of the ones shown by Bhatia, Lim, and Yamazaki.
Limin Zou, Yang Peng
doaj   +1 more source

A new positive definite geometric mean of two positive definite matrices [PDF]

, 1997
We introduce and study a new positive definite (in certain singular cases, positive semidefinite) geometric mean of two positive definite (under certain conditions, positive semidefinite ...
Miroslav Fiedler, Pták, Vlastimil, Vlastimil Pták, Fiedler, Miroslav   +3 more
core   +1 more source

Information Geometry of Positive Measures and Positive-Definite Matrices: Decomposable Dually Flat Structure

Entropy, 2014
Information geometry studies the dually flat structure of a manifold, highlighted by the generalized Pythagorean theorem. The present paper studies a class of Bregman divergences called the (ρ,τ)-divergence.
Shun-ichi Amari
doaj   +1 more source

Determinantal inequalities of Hua-Marcus-Zhang type for quaternion matrices

Open Mathematics, 2021
In this paper, the authors extend determinantal inequalities of the Hua-Marcus-Zhang type for positive definite matrices to the corresponding ones for quaternion matrices.
Hong Yan, Qi Feng
doaj   +1 more source

Determinantal inequalities for positive definite matrices

Discrete Mathematics, 1993
Several classical determinantal inequalities involving principal minors of a positive definite matrix are known. The authors consider the problem of identifying all such inequalities valid on all positive definite matrices and find some necessary and some sufficient conditions.
Charles R. Johnson, Wayne W. Barrett
openaire   +1 more source

Measuring Sphericity in Positive Semi-Definite Matrices

Axioms
The measure of sphericity for positive semi-definite matrices plays a crucial role in understanding their geometric properties, especially in high-dimensional settings.
Dário Ferreira, Sandra S. Ferreira
doaj   +1 more source

A Determinantal Inequality for Positive Definite Matrices [PDF]

Canadian Mathematical Bulletin, 1961
Let H = (Hi, j) (1 ≦ i, j ≦ n) be an nk × nk matrix with complex coefficients, where each Hi, j is itself a k × k matrix (n, k ≧ 2). Let |H| denote the determinant of H and let ∥H∥ = |(|H i, j|)| (1 ≦ i, j ≦ n ). The purpose of this note is to prove the following theorem.Theorem. If H is positive definite Hermitian then |H| ≦∥H∥. Moreover, |H| = ∥H∥ if
openaire   +2 more sources

SMARANDACHE SPECIAL DEFINITE ALGEBRAIC STRUCTURES [PDF]

, 2009
Introducing the notion of Smarandache special definite algebraic structures, also called equivalently as Smarandache definite special algebraic structures.
Vasantha, Kandasamy
core   +1 more source

Measurable diagonalization of positive definite matrices

Journal of Approximation Theory, 2014
In this paper we show that any positive definite matrix V with measurable entries can be written as V = U Lambda U*, where the matrix Lambda is diagonal, the matrix U is unitary, and the entries of U and Lambda are measurable functions (U* denotes the transpose conjugate of U). This result allows to obtain results about the zero location and asymptotic
Yamilet Quintana, José M. Rodríguez 0001   +1 more
openaire   +4 more sources

Re-visiting Riemannian geometry of symmetric positive definite matrices for the analysis of functional connectivity

NeuroImage, 2021
Common representations of functional networks of resting state fMRI time series, including covariance, precision, and cross-correlation matrices, belong to the family of symmetric positive definite (SPD) matrices forming a special mathematical structure ...
Kisung You, Hae-Jeong Park
doaj   +1 more source