The latent roots and vectors of a singular matrix

Abstract
In this paper a method is presented for calculating a square matrix W, of order r, from a square matrix A of order n and rank r, such that the latent roots of W are the non-zero latent roots of A, and the latent vectors of A can easily be obtained from the corresponding latent vectors of W. A modification of the method is also given so that W is symmetric when A is a positive semi-definite symmetric matrix.

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