Matrix equation AXB = E with PX = sXP constraint
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Abstract
The matrix equation AXB = E with the constraint PX = sXP is considered, where P is a given Hermitian matrix satisfying P 2 = I and s = ±1. By an eignvalue decomposition of P, the constrained problem can be equivalently transformed to a well-known unconstrained problem of matrix equation whose coefficient matrices contain the corresponding eigenvector, and hence the constrained problem can be solved in terms of the eigenvectors of P. A simple and eigenvector-free formula of the general solutions to the constrained problem by generalized inverses of the coefficient matrices A and B is presented. Moreover, a similar problem of the matrix equation with generalized constraint is discussed.
Keywords
eigenvalue decomposition constrained problem existence condition form of the solutionMR Subject Classification
15A06 15A18 15A23 15A24Preview
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© Editorial Committee of Applied Mathematics 2007