Abstract In this paper, we consider skew-Hermitian solution of coupled generalized Sylvester matrix equations encompassing $$*$$ ∗ -hermicity over complex field. The compact formula the general system is presented in terms inverses when some necessary and sufficient conditi...

We verify the skew weighing matrix conjecture for orders 2t .13, t 2:: 5, and give new results for 2t.15 proving the conjecture for t :2: 3.

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).

In this article, we present a high performance, portable and well templated implementation for computing fast-updating Pfaffian inverse of an even-ranked skew-symmetric (antisymmetric) matrix. It is achieved with skew-symmetric, blocked variant the Parlett-Reid algorithm update scheme based on Woodbury matrix identity. Installation framework into geminal-wavefunction-based many-variable Variati...

Let G be a collection of graphs with n vertices. We present a simple description of [G]χ = {H ∈ G : χ(H) = χ(G)} where χ denotes the Randić index. We associate to G a Q-linear map ρ : Qm → Qk (for some integers k, m depending on G) such that the kernel of ρ contains the necessary information to describe [G]χ in terms of linear equations. These results provide precise tools for analyzing the beh...

In this paper , the concept of the partition anti-circulant matrix on skew field is given,and its operational properties is discussed. Mathematics Subject Classification: 15A24