Symmetric solutions of linear matrix equations by matrix decompositions

Solving Linear Matrix Equations by Matrix Decompositions

In this paper, a system of linear matrix equations is considered. A new necessary and sufficient condition for the consistency of the equations is derived by means of the generalized singular-value decomposition, and the explicit representation of the general solution is provided. Keywords—Matrix equation, Generalized inverse, Generalized singular-value decomposition.

Least Squares Solutions of Inconsistent Fuzzy Linear Matrix Equations

New solution of fuzzy linear matrix equations

In this paper, a new method based on parametric form for approximate solu-tion of fuzzy linear matrix equations (FLMEs) of the form AX = B; where Ais a crisp matrix, B is a fuzzy number matrix and the unknown matrix X one,is presented. Then a numerical example is presented to illustrate the proposedmodel.

least squares solutions of inconsistent fuzzy linear matrix equations

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least squares solutions of inconsistent fuzzy linear matrix equations