A Correction to Colbourn's Paper on the Complexity of Matrix Symmetrizability

A square matrix A is transposable ii AT = PAQ for some ljermutation matrices P and Q, and symmiwizable if RA = ( RA)T for some permutation matrix R. A recent paper [I] purports to show that the matrix symmetrizability problem is isomorphism complete, that Is polynomial time equivalent to the graph isomorphism problem. Unfortunately, that paper is based on a misunderstanding about the contents of [4], as we shall indicate. In this r,ote we show that the matrix transposability problem is isomorphism complete, whereas the matrix symmetrizability problem is NPcomp!ete.