in this paper, we derive the necessary and sufficient conditions for the quaternion matrix equation xa=b to have the least-square bisymmetric solution and give the expression of such solution when the solvability conditions are met. futhermore, we consider the maximal and minimal inertias of the least-square bisymmetric solution to this equation. as applications, we derive sufficient and necess...

In this paper, we derive the necessary and sufficient conditions for the quaternion matrix equation XA=B to have the least-square bisymmetric solution and give the expression of such solution when the solvability conditions are met. Futhermore, we consider the maximal and minimal inertias of the least-square bisymmetric solution to this equation. As applications, we derive sufficient and necess...

In this paper, two matrix iterative methods are presented to solve the matrix equation A1X1B1 + A2X2B2 + ... + AlXlBl = C the minimum residual problem ‖ ∑l i=1 AiX̂iBi− C‖F = minXi∈BRni×ni‖ ∑l i=1 AiXiBi−C‖F and the matrix nearness problem [X̂1, X̂2, ..., X̂l] = min[X1,X2,...,Xl]∈SE ‖[X1, X2, ..., Xl] − [X̃1, X̃2, ..., X̃l]‖F , where BRni×ni is the set of bisymmetric matrices, and SE is the solution s...

A real n × n symmetric matrix X = (x i j)n×n is called a bisymmetric matrix if x i j = xn+1− j,n+1−i . Based on the projection theorem, the canonical correlation decomposition and the generalized singular value decomposition, a method useful for finding the least-squares solutions of the matrix equation AXA= B over bisymmetric matrices is proposed. The expression of the least-squares solutions ...

A1X = C1, A1X = C1, XB3 = C3, A2X = 62, to have bisymmetric solutions, and the system A1X = Ca, A3X B3 = C3, to have centrosymmetric solutions. The expressions of such solutions of the matrix and the systems mentioned above are also given. Moreover a criterion for a quaternion matrix to be bisymmetric is established and some auxiliary results on other sets over H are also mentioned. ~) 2005 Els...

BACKGROUND Whereas the majority of animals develop toward a predetermined body plan, plants show iterative growth and continually produce new organs and structures from actively dividing meristems. This raises an intriguing question: How are these newly developed organs patterned? In Arabidopsis embryos, radial symmetry is broken by the bisymmetric specification of the cotyledons in the apical ...

We provide sufficient conditions for a Sugeno integral to be bisymmetric. We explicitly describe bisymmetric Sugeno integrals over chains.

In this paper, we study the bisymmetric and skew solutions of quaternion generalized Lyapunov equation. With help semi-tensor product matrices, some new conclusions on expansion rules row column matrix matrices are proposed applied to calculation Using H-representation method, independent elements extracted according structural characteristics matrix, so as simplify operation process. Finally, ...