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.

The enhanced principal rank characteristic sequence (epr-sequence) of an n×n matrix is a sequence `1`2 · · ·`n, where each `k is A, S, or N according as all, some, or none of its principal minors of order k are nonzero. There has been substantial work on epr-sequences of symmetric matrices (especially real symmetric matrices) and real skew-symmetric matrices, and incidental remarks have been ma...

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.

Suppose that the matrix equation AXB = C with unknown matrix X is given, where A, B, and C are known matrices of suitable sizes. The matrix nearness problem is considered over the general and least squares solutions of the matrix equation AXB = C when the equation is consistent and inconsistent, respectively. The implicit form of the best approximate solutions of the problems over the set of sy...

We discuss a generalization of the Cohn–Umans method, a potent technique developed for studying the bilinear complexity of matrix multiplication by embedding matrices into an appropriate group algebra. We investigate how the Cohn–Umans method may be used for bilinear operations other than matrix multiplication, with algebras other than group algebras, and we relate it to Strassen’s tensor rank ...

the matrix functions appear in several applications in engineering and sciences. the computation of these functions almost involved complicated theory. thus, improving the concept theoretically seems unavoidable to obtain some new relations and algorithms for evaluating these functions. the aim of this paper is proposing some new reciprocal for the function of block anti diagonal matrices. more...

We introduce a notion of left-symmetric bialgebra which is an analogue of the notion of Lie bialgebra. We prove that a left-symmetric bialgebra is equivalent to a symplectic Lie algebra with a decomposition into a direct sum of the underlying vector spaces of two Lagrangian subalgebras. The latter is called a parakähler Lie algebra or a phase space of a Lie algebra in mathematical physics. We i...