Capelli's identity

English

Etymology

Named after Alfredo Capelli (1887).

Proper noun

Capelli's identity

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