The Hungarian physicist Eugene Wigner introduced random matrix models in physics to describe the energy spectra of atomic nuclei. As such, main goal theory (RMT) has been derive eigenvalue statistics matrices drawn from a given distribution. approach gives powerful insights into properties complex, chaotic systems thermal equilibrium. Another Hungarian, Cornelius Lanczos, suggested method reduc...

Let M(A) denote the comparison matrix of a square H-matrix A, that is, M(A) is an M-matrix. Hmatrices such that their comparison matrices are non-singular are well studied in the literature. In this paper, we study characterizations of H-matrices with either singular or non-singular comparison matrices. The spectral radius of the Jacobi matrix of M(A) and the generalized diagonal dominance prop...

In this paper, complex singular Wishart matrices and their applications are investigated. In particular, a volume element on the space of positive semidefinite m×m complex matrices of rank n < m is introduced and some transformation properties are established. The Jacobian for the change of variables in the singular value decomposition of general m × n complex matrices is derived. Then the dens...