This article is cited in 2 papers

New polynomial identities for determinants over commutative rings

G. P. Egorychev

Siberian Federal University, 26, Kirenskogo St., Krasnoyarsk, 660074

Abstract: Let $K$ be a commutative ring with division by integers. Here we give a new family of polynomial identities (calculation formulas) for determinants over the ring $K$ using the well-known polarization theorem, which allows us a new criterian for linear independence of $n$ vectors in $\mathbb{C}^{n}$.

Keywords: determinants; commutative rings; polynomial identities.

UDC: 512.64+512.55