The singular values of XY − Y X are the objects under investigation. Here, X and Y are square matrices with complex entries, and one of them has rank one. Hence, there are at most two non-trivial numbers among the commutator’s singular values, and the pairs of interest can be depicted in the plane. The emphasis will lie on the unexpectedly intriguing case in which both matrices are of rank one ...

In this paper, we consider how eigenvalues of a matrix A change when it is perturbed to e A = D 1AD2 and how singular values of a (nonsquare) matrix B change when it is perturbed to e B = D 1BD2, where D1 and D2 are assumed to be close to unitary matrices of suitable dimensions. We have been able to generalize many well-known perturbation theorems, including Ho man-Wielandt theorem and Weyl-Lid...

The standard (point-wise) linear channel model for MIMO wireless systems provides a simplistic mapping from antenna elements to continuous (operator) view point of wireless channels. Low-rank, high-dimension sampling matrices generated by Ray-Tracing may be used to estimate (with error) the “true” operator channel. In order to achieve reasonable estimation error bounds, intractably large dimens...

We study the asymptotic behavior of outliers in the spectrum of bounded rank perturbations of large random matrices. In particular, we consider perturbations of elliptic random matrices which generalize both Wigner random matrices and non-Hermitian random matrices with iid entries. As a consequence, we recover the results of Capitaine, Donati-Martin, and Féral for perturbed Wigner matrices as w...