Error-free matrix symmetrizers and equivalent symmetric matrices

Abstract

A symmetrizer of the matrix A is a symmetric solution X that satisfies the matrix equation XA=A′X. An exact matrix symmetrizer is computed by obtaining a general algorithm and superimposing a modified multiple modulus residue arithmetic on this algorithm. A procedure based on computing a symmetrizer to obtain a symmetric matrix, called here an equivalent symmetric matrix, whose eigenvalues are the same as those of a given real nonsymmetric matrix is presented.