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.

triangular matrix, powers of triangular matrix, series of triangular matrices, complete homogeneous symmetric polynomials

Received: March 1, 2025; Accepted: April 9, 2025; Published: May 31, 2025

How to cite this article: E. F. Cornelius, Jr., Triangular matrices and complete homogeneous symmetric polynomials, JP Journal of Algebra, Number Theory and Applications 64(4) (2025), 417-431. https://doi.org/10.17654/0972555525022

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License