منابع مشابه
On the Approximation of Matrix Products and Positive Definite Matrices
In this paper, we introduce and analyze new randomized and deterministic algorithms to approximate the product of two matrices. In addition we provide what is, to the best of our knowledge, the first relative error bound for the Nyström approximation of quadratic forms. While deriving the proofs of the results, we highlight several new connections between matrix products, the Nyström extension ...
متن کاملON 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 کاملProduct of three positive semi-definite matrices
In [2], the author showed that a square matrix with nonnegative determinant can always be written as the product of five or fewer positive semi-definite matrices. This is an extension to the result in [1] asserting that every matrix with positive determinant is the product of five or fewer positive definite matrices. Analogous to the analysis in [1], the author of [2] studied those matrices whi...
متن کاملWasserstein Riemannian Geometry of Positive-definite Matrices∗
The Wasserstein distance on multivariate non-degenerate Gaussian densities is a Riemannian distance. After reviewing the properties of the distance and the metric geodesic, we derive an explicit form of the Riemannian metrics on positive-definite matrices and compute its tensor form with respect to the trace scalar product. The tensor is a matrix, which is the solution of a Lyapunov equation. W...
متن کاملRiemannian Sparse Coding for Positive Definite Matrices
Inspired by the great success of sparse coding for vector valued data, our goal is to represent symmetric positive definite (SPD) data matrices as sparse linear combinations of atoms from a dictionary, where each atom itself is an SPD matrix. Since SPD matrices follow a non-Euclidean (in fact a Riemannian) geometry, existing sparse coding techniques for Euclidean data cannot be directly extende...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1967
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1967.23.427