Narrow Results

We provide a lightweight algorithm to express each of the elementary symmetric polynomials as a linear combination of (products of) power sum symmetric polynomials and, also, the power sums purely in terms of the elementary symmetric polynomials. Our method does not use Newton’s identities, which give such relations only implicitly. Each identity in the sequence is generated through a single differentiation.

The Cayley–Hamilton–Newton theorem for half-quantum matrices is proven.