A norm inequality for positive block matrices

A Norm Compression Inequality for Block Partitioned Positive Semidefinite Matrices

where B and D are square blocks. We prove the following inequalities for the Schatten q-norm ||.||q , which are sharp when the blocks are of size at least 2× 2: ||A||q ≤ (2 q − 2)||C||q + ||B|| q q + ||D|| q q, 1 ≤ q ≤ 2, and ||A||q ≥ (2 q − 2)||C||q + ||B|| q q + ||D|| q q, 2 ≤ q. These bounds can be extended to symmetric partitionings into larger numbers of blocks, at the expense of no longer...

A norm inequality for pairs of commuting positive semidefinite matrices

A NORM INEQUALITY FOR CHEBYSHEV CENTRES

In this paper, we study the Chebyshev centres of bounded subsets of normed spaces and obtain a norm inequality for relative centres. In particular, we prove that if T is a remotal subset of an inner product space H, and F is a star-shaped set at a relative Chebyshev centre c of T with respect to F, then llx - qT (x)1I2 2 Ilx-cll2 + Ilc-qT (c) 112 x E F, where qT : F + T is any choice functi...

On a Norm Compression Inequality for 2 ×N Partitioned Block Matrices

We conjecture the following so-called norm compression inequality for 2×N partitioned block matrices and the Schatten p-norms: for p ≥ 2,

A determinantal inequality for positive semidefinite matrices

Let A,B,C be n× n positive semidefinite matrices. It is known that det(A+ B + C) + detC ≥ det(A+ C) + det(B + C), which includes det(A+B) ≥ detA+ detB as a special case. In this article, a relation between these two inequalities is proved, namely, det(A+ B + C) + detC − (det(A+ C) + det(B + C)) ≥ det(A+ B)− (detA+ detB).