In this article the unitary equivalence transformation of normal matrices to tridiagonal form is studied. It is well-known that any matrix is unitarily equivalent to a tridiagonal matrix. In case of a normal matrix the resulting tridiagonal inherits a strong relation between its superand subdiagonal elements. The corresponding elements of the superand subdiagonal will have the same absolute val...

We explain and justify a path-following algorithm for solving the equations Af^ix) = a, where A is a. linear transformation from R" to R", C is a polyhedral convex subset of R", and Ac is the associated normal map. When A^ is coherently oriented, we are able to prove that the path following method terminates at the unique solution of A^ix) = a, which is a generalization of the weU known fact th...

where n is the forcing function. In our problems, the mass and stiffness matrices are symmetric with the former semidefinite and the latter being positive definite. (We have ignored the damping term for now but it will be relevant in future.) The forcing function n is a product of a vector f that specifies the spatial distribution of the force and a scalar function g(t) that governs the tempora...

We study the genuine multipartite entanglement in tripartite quantum systems. By using Schmidt decomposition and local unitary transformation, we convert general states to simpler forms consider certain matrices from correlation tensors Bloch representation of simplified density matrices. Using these special matrices, obtain new criteria for entanglement. Detail examples show that our are able ...

A similarity transformation is obtained between general population matrices models of the Usher or Lefkovitch types and a simpler model, the pseudoLeslie model. The pseudo Leslie model is a matrix that can be decomposed in a row matrix, which is not necessarily non-negative and a subdiagonal positive matrix. This technique has computational advantages, since the solutions of the iterative probl...

Toeplitz matrices have found important applications in bioinformatics and computational biology [5, 6, 11, 12]. In this paper we concern the spectral properties of hermitian Toeplitz matrices. Based on the fact that every centrohermitian matrix can be reduced to a real matrix by a simple similarity transformation, we first consider the eigenstructure of hermitian Toeplitz matrices and then disc...

The QR-algorithm is a renowned method for computing all eigenvalues of an arbitrary matrix. A preliminary unitary similarity transformation to Hessenberg form is indispensable for keeping the computational complexity of the subsequent QR-steps under control. In this paper, a whole new family of matrices, sharing the major qualities of Hessenberg matrices, will be put forward. This gives rise to...

when un = 22"-o a-inUi for all ra^O. If the sequence to sequence transformation associated with A is such that [u/[ ] exists and converges whenever [un] converges we call A a K matrix. If [uJ ] exists and converges to limn,,, un whenever this limit exists we call A a T matrix. Similar names for the series to sequence and the series to series matrices are TCi, 7\ and K2, T2 matrices respectively...

Toeplitz matrices have been found important applications in bioinformatics and computational biology [5-9, 11-12]. In this paper we concern the reconstruction of an hermitian Toeplitz matrices with prescribed eigenpairs. Based on the fact that every centrohermitian matrix can be reduced to a real matrix by a simple similarity transformation, we first consider the eigenstructure of hermitian Toe...

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...