On the class of <f>Dk</f>-symmetrizable matrices

It is known that for every real square matrix A there exists a nonsingular real symmetric matrix S such thatSA=A′S,where <f>A′</f> denotes the transpose of A.Using the notion of an M-matrix we derive a criterion for A to satisfy the above equality with a diagonal S of signature k. Such a matrix A will be called <f>Dk</f>-symmetrizable and the paper presents some results on this concept. In particular we show that a <f>Dk</f>-symmetrizable matrix shares many properties with a real symmetric matrix and that any real matrix A, up to an orthogonal similarity, is <f>Dk</f>-symmetrizable for some k. [Copyright &y& Elsevier]