On the Latent Roots of Certain Matrices

Abstract

In the present note certain known theorems on the latent roots of matrices are deduced from the fundamental theorem that a matrix A can be expressed in the form PQP-1, where P is non-singular and Q has zero elements everywhere to the left of the principal diagonal, and the latent roots of A in the diagonal. [The presence or absence of non-zero elements to the right of the diagonal is known to depend on the nature of the “elementary divisors” of the “characteristic determinant” of A, but in what follows these will not concern us.]