In this paper we focus on the maximization of Rayleigh Quotients. It is very well known that a Rayleigh Quotient's maximum value is the greatest eigenvalue of its numerator core matrix under the weighing of its denominator core matrix. Here we use core matrices which is are somehow the matrix representation of an algebraic multiplication operator whose action on its operand is simply multiplication by a function, univariate or multivariate. Hence the basic process is the evaluation of the greatest eigenvalue and the corresponding eigenvector. In the univariate case this process can be handled in accordance with the type and characteristic of the matrix but in multivariate case this issue may become more complicated. For that reason here we develop a quite new technique which factorizes the multivariate Rayleigh Quotient to univariate ratios and deal with the optimization of the univariate parts instead of tackling with the whole multivariate structure, by using Direct Product of the matrices.