A more general solution and a new didactic demonstration of the maximization of the multidimensional case of the Generalized Rayleigh Quotient are described. This solution will not only be the well-known eigenvectors solution widely available in the literature hut also a general transformation that is not necessarily orthogonal. The demonstration uses only basic linear algebra and simple lagrangian maximization to find the transformation matrix that maximizes the multidimensional Generalized Rayleigh Quotient for Linear Discriminant Analysis, widely used in signal classification applications.
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