On The Frobenius Condition Number of Positive Definite Matrices

On The Frobenius Condition Number of Positive Definite Matrices

Minimal condition number for positive definite Hankel matrices using semidefinite programming

Article history: Received 27 January 2009 Accepted 15 April 2010 Available online 26 June 2010 Submitted by V. Mehrmann

Positive definite matrix approximation with condition number constraint

Positive definite matrix approximation with a condition number constraint is an optimization problem to find the nearest positive definite matrix whose condition number is smaller than a given constant. We demonstrate that this problem can be converted to a simpler one in this note when we use a unitary similarity invariant norm as a metric. We can especially convert it to a univariate piecewis...

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...

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.