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

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...

We extend the Golub-Kahan algorithm for computing the singular value decomposition of bidiagonal matrices to triangular matrices R. Our algorithm avoids the explicit formation of R T R or RRT. We derive a relation between left and right singular vectors of triangular matrices and use it to prove monotonic convergence of singular values and singular vectors. The convergence rate for singular val...

In this paper, we first give a lower and upper bounds for singular values of a 2×2 positive semidefinite block matrices. Then, we give some weakly majorization inequalities of singular values positive semidefinite block matrices. Also, we present inequalities involving the direct sum and sum of positive semidefinite matrices.

Two issues concerning the construction of square matrices with prescribed singular values and eigenvalues are addressed. First, a necessary and sufficient condition for the existence of an n × n complex matrix with n given nonnegative numbers as singular values and m(≤ n) given complex numbers to be m of the eigenvalues is determined. This extends the classical result of Weyl and Horn treating ...

In this paper we will generalize a singular value inequality that was proved before. In particular we obtain an inequality for numerical radius as follows: begin{equation*} 2 sqrt{t (1-t)} omega(t A^{nu}B^{1-nu}+(1-t)A^{1-nu}B^{nu}) leq omega(t A + (1- t) B), end{equation*} where, $ A $ and $ B $ are positive semidefinite matrices, $ 0 leq t leq 1 $ and $ 0 leq nu leq frac{3}{2}.$