a i f e

F. A matrix A is called positive definite if all of its eigenval-ric systems can be transformed into equivalent symmetric systems so that one can take advantage of the well-developed theories for symmetric systems to analyze them. This is the primary reason to study ‘‘symmetrizability’ ’ of asymmetric systems. In linear dy-namics literature symmetrizability has been addressed by similar-ity transformation based on Taussky’s @10 # definition. We call Taussky’s approach of symmetrization by similarity transforma-tion as ‘‘symmetrization of first kind.’ ’ In this paper symmetriz-ability of a matrix is redefined in the context of equivalence trans-formation. Such symmetrization will be called ‘‘symmetrization of second kind.’’ Equivalence transformations are the most general class of non-ues l i.0 and will be denoted by A.0. A unit matrix IPRN3N is a diagonal matrix with all diagonal entries equal to one. Let