NEW EXPRESSIONS FOR THE SOLUTION OF THE MATRIX EQUATION A(T)X+XA=H

The matrix equation AX+XA = H where A is symmetric appears in a variet y of problems in continuum mechanics and other subjects. Several forms of the solution are available in the literature. We present new solut ions which appear to be more concise. This is achieved by employing th e adjoint matrix (A) over cap of A whose elements are the cofactors of A, and by considering the solutions to the symmetric and skew-symmetr ic parts of H separately. The derivation is no more complicated if we consider the more general matrix equation A(T) X + XA = H in which A n eed not be symmetric, and the superscript T denotes the transpose. The main results are shown in (2.6), (3.2), (4.14a,b) and (5.1a,b) for th e three-dimensional case and in (6.6a,b) for the two-dimensional case.