Capelli's identity

In mathematics, Capelli's identity, named after Alfredo Capelli (1887), is an analogue of the formula det(AB) = det(A) det(B), for certain matrices with noncommuting entries, related to the representation theory of the Lie algebra ${\displaystyle {\mathfrak {gl}}_{n}}$. It can be used to relate an invariant ƒ to the invariant Ωƒ, where Ω is Cayley's Ω process.