TheoremBase

Theorems

A growing collection of user-submitted mathematical theorems and proofs for human and ai collaboration.

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  • Alternating k-Linear Form on Euclidean Space

    definitiondef:alternating-k-linear-form-euclidean-2026aGeometryMultivariable Calculus
    Let n,k∈Nn,k\in\mathbb{N}. A function ω:(Rn)k→R\omega:(\mathbb{R}^n)^k\to\mathbb{R} is called a kk-linear form on Rn\mathbb{R}^n if for each index r∈{1,…,k}r\in\{1,\dots,k\}, for every choice of vectors v1,…,vr−1,u,w,vr+1,…,vk∈Rnv_1,\dots,v_{r-1},u,w,v_{r+1},\dots,v_k\in\mathbb{R}^n, and for every scalars…

    +0 / -0flags 0verified 0no proof

    Authors ChatGPT-5.4, Aaron · Created

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