For a matrix A = [aij ] m,n i,j=1 ∈ Fm×n, the transpose of A is the matrix A> = [aji] n,m j,i=1 ∈ Fn×m. A square matrix A ∈ Rn×n is called symmetric if aji = aij for all i, j ∈ {1, . . . , n} and is called skew-symmetric or anti-symmetric if aji = −aij for all i, j ∈ {1, . . . , n}. A basis will be denoted B = {u1,u2, . . . ,un} when the ordering of the basis vectors is not important and B = [u...

In this paper we consider numerical methods for computing functions of matrices being Hamiltonian and skew-symmetric. Analytic functions of this kind of matrices (i.e., exponential and rational functions) appear in the numerical solutions of orthosymplectic matrix differential systems when geometric integrators are involved. The main idea underlying the presented techniques is to exploit the sp...

For a given real invertible skew-symmetric matrix H, we characterize the real 2n×2n matrices X that allow an H-Hamiltonian polar decomposition of the type X = UA, where U is a real H-symplectic matrix (UTHU = H) and A is a real H-Hamiltonian matrix (HA = −ATH).

1. Unitary Geometry on Exceptional Cartan Domains In 1935, E.Cartan classified all symmetric bounded domains. He prived that there exit only six types of irreducible bounded symmetric domains in C. They can be realized as follows: RI(m,n) = {Z ∈ Cmn|I − ZZ ′ > 0, Z − (m,n) matrix} RIIp = {Z ∈ Cp(p+1)/2|I − ZZ ′ > 0, Z − symmetric matric of degree p} RIIIq = {Z ∈ Cq(q−1)/2|I − ZZ ′ > 0, Z − skew...

We derive the necessary and sufficient conditions of and the expressions for the orthogonal solutions, the symmetric orthogonal solutions, and the skew-symmetric orthogonal solutions of the system of matrix equations AX B and XC D, respectively. When the matrix equations are not consistent, the least squares symmetric orthogonal solutions and the least squares skewsymmetric orthogonal solutions...

We extend the correspondence between double Lie algebras and skew-symmetric Rota-Baxter operators of weight 0 on matrix algebra for infinite-dimensional case. give first example a simple algebra.

Canonical forms for matrix triples (A,G, Ĝ), where A is arbitrary rectangular andG, Ĝare either real symmetric or skew symmetric, or complex Hermitian or skew Hermitian, arederived. These forms generalize classical singular value decompositions. In [1] a similarcanonical form has been obtained for the complex case. In this paper, we provide analternative proof for the comple...

Two algorithmic techniques for specifying the existence of a k×k submatrix with elements 0,±1 in a skew and symmetric conference matrix of order n are described. This specification is achieved using an appropriate computer algebra system.