in this paper we consider the solutions of linear systems of saddle point problems‎. ‎by using the spectrum of a quadratic matrix polynomial‎, ‎we study the eigenvalues of the iterative matrix of the hermitian and skew hermitian splitting method‎.

‎‎A natural generalization of two dimensional cyclic code ($T{TDC}$) is two dimensional skew cyclic code‎. ‎It is well-known that there is a correspondence between two dimensional skew cyclic codes and left ideals of the quotient ring $R_n:=F[x,y;rho,theta]/_l$‎. ‎In this paper we characterize the left ideals of the ring $R_n$ with two methods and find the generator matrix for two dimensional s...

The authors show that there is a generalization of Rodrigues’ formula for computing the exponential map exp: so(n)→SO(n) from skewsymmetric matrices to orthogonal matrices when n ≥ 4, and give a method for computing some determination of the (multivalued) function log: SO(n) → so(n). The key idea is the decomposition of a skew-symmetric n×n matrix B in terms of (unique) skew-symmetric matrices ...

A square matrix is principally unimodular if every principal submatrix has determinant 0 or 1. Let A be a symmetric (0; 1)-matrix, with a zero diagonal. A PU-orientation of A is a skew-symmetric signing of A that is PU. If A 0 is a PU-orientation of A, then, by a certain decomposition of A, we can construct every PU-orientation of A from A 0. This construction is based on the fact that the PU-o...

We extend results concerning orthogonal matrices to a more general class of matrices that will be called P -orthogonal. This is a large class of matrices that includes, for instance, orthogonal and symplectic matrices as particular cases. We study the elementary properties of P -orthogonal matrices and give some exponential representations. The role of these matrices in matrix decompositions, w...

Most eigenvalue problems arising in practice are known to be structured. Structure is often introduced by discretization and linearization techniques but may also be a consequence of properties induced by the original problem. Preserving this structure can help preserve physically relevant symmetries in the eigenvalues of the matrix and may improve the accuracy and efficiency of an eigenvalue c...

— In this paper, we consider the problem of deriving new eigenvalue distributions of real-valued Wishart matrices that arises in many scientific and engineering applications. The distributions are derived using the tools from the theory of skew symmetric matrices. In particular, we relate the multiple integrals of a determinant, which arises while finding the eigenvalue distributions, in terms ...