The sums of powers as simultaneous canonical expressions

Abstract

1. In this paper I discuss the expression of m + 1 general forms F, F′, …, F(m), each of order n and homogeneous in r + 1 variables z0, z1, …, zl, …, zr, as the sums each of the nth powers of (the same) h + H linear forms in these variables. I take h > 0 of these linear forms to be undetermined, namely the formswhose coefficients are undetermined; and I take the remaining H ≥ 0 linear forms to be assigned, namely the formswhose coefficients are assigned.