The Generalized Bisymmetric (Bi-Skew-Symmetric) Solutions of a Class of Matrix Equations and Its Least Squares Problem

Least Squares Solutions of Inconsistent Fuzzy Linear Matrix Equations

Least-Squares Solutions of the Matrix Equation AXA= B Over Bisymmetric Matrices and its Optimal Approximation

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 ...

least squares solutions of inconsistent fuzzy linear matrix equations

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least squares solutions of inconsistent fuzzy linear matrix equations

The (R,S)-symmetric and (R,S)-skew symmetric solutions of the pair of matrix equations A1XB1 = C1 and A2XB2 = C2

Let $Rin textbf{C}^{mtimes m}$ and $Sin textbf{C}^{ntimes n}$ be nontrivial involution matrices; i.e., $R=R^{-1}neq pm~I$ and $S=S^{-1}neq pm~I$. An $mtimes n$ complex matrix $A$ is said to be an $(R, S)$-symmetric ($(R, S)$-skew symmetric) matrix if $RAS =A$ ($ RAS =-A$). The $(R, S)$-symmetric and $(R, S)$-skew symmetric matrices have a number of special properties and widely used in eng...