Rajendra Bhatia

More matrix forms of the arithmetic-geometric mean inequality

For arbitrary

Notes on matrix arithmetic-geometric mean inequalities

n times n

On the exponential metric increasing property

matrices A, B, X, and for every unitarily invariant norm, it is proved that

Clarkson Inequalities with Several Operators

2|||A^ * XB|||leqq |||AA^ * X + XBB^ * |||

Cartesian decompositions and Schatten norms

.

Compact operators whose real and imaginary parts are positive

Abstract For positive semi-definite n×n matrices, the inequality 4|||AB|||⩽|||(A+B) 2 ||| isshown to hold for every unitarily invariant norm. The connection of this with some other matrix arithmetic–geometric mean inequalities and trace inequalities is discussed.

Riemannian geometry and matrix geometric means

A short and simple proof is given for the inequality that shows that positive definite matrices constitute a Riemannian manifold of negative curvature. The idea of the proof leads to generalisations to non-Riemannian metrics, and to connections with some well-known inequalities of mathematical physics.

Norm inequalities for partitioned operators and an application

Several inequalities for trace norms of sums of

The matrix arithmetic-geometric mean inequality revisited

n

Norm inequalities related to the matrix geometric mean

operators with roots of unity coefficients are proved in this paper. When n=2, these reduce to the classical Clarkson inequalities and their non-commutative analogues.