TRIANGULAR MATRICES AND COMPLETE HOMOGENEOUS SYMMETRIC POLYNOMIALS

In [1], the authors computed the powers of the real upper triangular matrices, and demonstrated that the resulting matrices have complete homogeneous symmetric polynomials as entries. Those results are extended to infinite matrices and to infinite series of matrices over integral domains. The inverses of the are computed, as are powers of the inverses. The results also are used to produce new proofs of a famous result about complete homogeneous symmetric polynomials, without the use of generating functions.