Let ‖| · ‖| be any give unitarily invariant norm. We obtain some exponential relations in the context of semisimple Lie group. On one hand they extend the inequalities (1) ‖|e‖| ≤ ‖|eReA‖| for all A ∈ Cn×n, where ReA denotes the Hermitian part of A, and (2) ‖|e‖| ≤ ‖|ee‖|, where A and B are n×n Hermitian matrices. On the other hand, the inequalities of Weyl, Ky Fan, Golden-Thompson, Lenard-Thom...

We investigate the spectral fluctuation properties of constrained ensembles of random matrices (defined by the condition that a number NQ of matrix elements vanish identically; that condition is imposed in unitarily invariant form) in the limit of large matrix dimension. We show that as long as NQ is smaller than a critical value (at which the quadratic level repulsion of the Gaussian unitary e...

The unitarily invariant probability measures on infinite Hermitian matrices have been classified by Pickrell, and Olshanski Vershik. This classification is equivalent to determining the boundary of a certain inhomogeneous Markov chain with given transition probabilities. formulation problem makes sense for general $\beta$-ensembles when one takes as probabilities Dixon-Anderson conditional dist...

A unitarily invariant projective framework is introduced to analyze the complexity of path–following methods for the eigenvalue problem. A condition number, and its relation to the distance to ill–posedness, is given. A Newton map appropriate for this context is defined, and a version of Smale’s γ-Theorem is proven. The main result of this paper bounds the complexity of path–following methods i...

We discuss certain aspects of random multi-matrix models: random matrices chosen at random according to a certain unitarily invariant Gibbs measure on the space of N × N matrices. Thanks to work of Voiculescu, Biane, Guionnet and others, free probability tools can be used to analyze the limiting behavior of such random matrix models. In addition to touching upon a connection between such random...

It is shown that for many finite dimensional normed vector spaces V over C, a linear projection P : V → V will have nice structure if P + λ(I − P ) is an isometry for some complex unit not equal to one. From these results, one can readily determine the structure of bicircular projections, i.e., those linear projections P such that P + μ(I − P ) is a an isometry for every complex unit μ. The key...

This paper characterizes the performance of massive multiuser spatial modulation MIMO systems, when a regularized form least-squares method is used for detection. For generic distortion function and right unitarily invariant channel matrices, per-antenna transmit rate asymptotic achieved by this class detectors are derived. Invoking an characterization, we address two particular applications. N...