Monte Carlo estimators for the Schatten p-norm of symmetric positive semidefinite matrices

Singular value inequalities for positive semidefinite matrices

In this note‎, ‎we obtain some singular values inequalities for positive semidefinite matrices by using block matrix technique‎. ‎Our results are similar to some inequalities shown by Bhatia and Kittaneh in [Linear Algebra Appl‎. ‎308 (2000) 203-211] and [Linear Algebra Appl‎. ‎428 (2008) 2177-2191]‎.

A norm inequality for pairs of commuting positive semidefinite 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...

singular value inequalities for positive semidefinite matrices

in this note‎, ‎we obtain some singular values inequalities for positive semidefinite matrices by using block matrix technique‎. ‎our results are similar to some inequalities shown by bhatia and kittaneh in [linear algebra appl‎. ‎308 (2000) 203-211] and [linear algebra appl‎. ‎428 (2008) 2177-2191]‎.

A Sparse Decomposition of Low Rank Symmetric Positive Semidefinite Matrices

Suppose that A ∈ RN×N is symmetric positive semidefinite with rank K ≤ N . Our goal is to decompose A into K rank-one matrices ∑K k=1 gkg T k where the modes {gk} K k=1 are required to be as sparse as possible. In contrast to eigen decomposition, these sparse modes are not required to be orthogonal. Such a problem arises in random field parametrization where A is the covariance function and is ...