The central limit theorem on spaces of positive definite matrices

نویسندگان

چکیده

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

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 Einstein and M"{o}bius gyrovector spaces‎. ‎We introduce the structure of gyrovector space and the gyroline on the open convex cone of positive definite matrices and explore its...

متن کامل

Deconvolution Density Estimation on Spaces of Positive Definite Symmetric Matrices

Motivated by applications in microwave engineering and diffusion tensor imaging, we study the problem of deconvolution density estimation on the space of positive definite symmetric matrices. We develop a nonparametric estimator for the density function of a random sample of positive definite matrices. Our estimator is based on the Helgason-Fourier transform and its inversion, the natural tools...

متن کامل

ON f-CONNECTIONS OF POSITIVE DEFINITE MATRICES

In this paper, by using Mond-Pečarić method we provide some inequalities for connections of positive definite matrices. Next, we discuss specifications of the obtained results for some special cases. In doing so, we use α-arithmetic, α-geometric and α-harmonic operator means.

متن کامل

Riemannian geometry on positive definite matrices

The Riemannian metric on the manifold of positive definite matrices is defined by a kernel function φ in the form K D(H,K) = ∑ i,j φ(λi, λj) −1TrPiHPjK when ∑ i λiPi is the spectral decomposition of the foot point D and the Hermitian matrices H,K are tangent vectors. For such kernel metrics the tangent space has an orthogonal decomposition. The pull-back of a kernel metric under a mapping D 7→ ...

متن کامل

Central Limit Theorem for Products of Random Matrices

Using the semigroup product formula of P. Chernoff, a central limit theorem is derived for products of random matrices. Applications are presented for representations of solutions to linear systems of stochastic differential equations, and to the corresponding partial differential evolution equations. Included is a discussion of stochastic semigroups, and a stochastic version of the Lie-Trotter...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Journal of Multivariate Analysis

سال: 1989

ISSN: 0047-259X

DOI: 10.1016/0047-259x(89)90031-6