The main concern of this paper is the Karcher mean of linearly independent triples (A,B,C) on the hyperbolic manifold of 2×2 positive definite matrices of determinant 1. We show that the Karcher mean is of the form ...

We present a classification of 2×2 positive definite Hermitian triples of determinant one having the Karcher mean formula [Formula presented]. We further show that it is equivalent to the trace condition: tr(AB−1)=tr(AC− ...

The modern GPUs are well suited for intensive computational tasks and massive parallel computation. Sparse matrix multiplication and linear triangular solver are the most important and heavily used kernels in scientific ...

Given two positive definite matrices A and B, a well known result by Gelfand, Naimark and Lidskii establishes a relationship between the eigenvalues of A and B and those of AB by means of majorization inequalities. In this ...

The celebrated Heinz inequality asserts that 2|||A^1/2XB^1/2||| leq|||A^νXB^(1−ν)+ A^(1−ν)XB^ν||| leq |||AX + XB||| for X ∈ B(H ), A,B ∈B(H )_+, every unitarily invariant norm ||| · ||| and ν ∈ [0,1]. In this paper, we ...

Given a Hermitian matrices A∈C^n×n and D∈C^m×m, and k > 0, we characterize under which conditions there exists a matrix K∈C^n×m with ∥K∥ < k such that the non-Hermitian block-matrix [AK∗A−AKD] has a positive (semi-) definite ...