Capelli's identity

proper noun

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 glₙ. It can be used to relate an invariant ƒ to the invariant Ωƒ, where Ω is Cayley's Ω process.

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Meanings

proper noun
  1. mathematicsAn 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 glₙ. It can be used to relate an invariant ƒ to the invariant Ωƒ, where Ω is Cayley's Ω process.

Origin

Named after Alfredo Capelli (1887).

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Cite this entry
APA

Capelli's identity. (n.d.). In WatkinsX Dictionary. Retrieved November 4, 2026, from https://dictionary.watkinsx.com/word/Capelli's%20identity

MLA

“Capelli's identity.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/Capelli's%20identity. Accessed November 4, 2026.

Chicago

WatkinsX Dictionary, s.v. “Capelli's identity,” accessed November 4, 2026, https://dictionary.watkinsx.com/word/Capelli's%20identity.

Source: Capelli's identity on Wiktionary, CC BY-SA 4.0.