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Published online by Cambridge University Press: 20 January 2009
The present note contains generalisations and new proofs of certain theorems in the theory of Young Tableaux and Invariant Matrices. For an account of Young Tableaux and their applications, and an introduction to the method of Clebsch-Aronhold symbols, reference should be made to Rutherford [1], and Turnbull [1], respectively. An invariant matrix T(A) of a given square matrix A is, as appears from the context in § 4 below, a matrix of polynomials in the elements of A, regarded as independent variables, such that T(AB) = T(A) T(B). Further details, and references to original sources, are given in Wallace [1].