Complementarity properties of singular M-matrices

Singular values of convex functions of matrices

‎Let $A_{i},B_{i},X_{i},i=1,dots,m,$ be $n$-by-$n$ matrices such that $‎sum_{i=1}^{m}leftvert A_{i}rightvert ^{2}$ and $‎sum_{i=1}^{m}leftvert B_{i}rightvert ^{2}$  are nonzero matrices and each $X_{i}$ is‎ ‎positive semidefinite‎. ‎It is shown that if $f$ is a nonnegative increasing ‎convex function on $left[ 0,infty right) $ satisfying $fleft( 0right)‎ ‎=0 $‎, ‎then  $$‎2s_{j}left( fleft( fra...

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]‎.

More about measures and Jacobians of singular random matrices

In this work are studied the Jacobians of certain singular transformations and the corresponding measures which support the jacobian computations.

Two modified Jacobi methods for M-matrices

Singular Mueller matrices.

Singular Mueller matrices play an important role in polarization algebra and have peculiar properties that stem from the fact that either the medium exhibits maximum diattenuation and/or polarizance or because its associated canonical depolarizer has the property of fully randomizing the circular component (at least) of the states of polarization of light incident on it. The formal reasons for ...