An exterior-algebraic proof of Newton's formulae (Q582350)

This paper offers a direct proof of Newton's formula in the theory of symmetric polynomials in terms of exterior algebra, i.e. \(rI_ r+I_{r- 1}tr(-A)+...+I_ 1tr(-A)^{r-1}+I_ 0tr(-A)^ r=0,\) \(I_ ntr(- A)^{r-n}+I_{n-1}tr(-A)^{r-(n-1)}+...+I_ 1tr(-A)^{r-1}+I_ 0tr(-A)^ r=0,\) where A is a second order tensor on an n-dimensional space, \(I_ 1,I_ 2,...,I_ n\) are n principal invariants of A and \(I_ 0:=1\). No direct proof of Newton's formulae are available, as the author declares.