Reciprocal basis

Let $𝑉$ be a vector space equipped with a nondegenerate bilinear form $⟨ ?, ? ⟩$ . Given a basis ${𝑣 𝑖} 𝑛 𝑖 = 1$ , the reciprocal basis is a unique basis ${𝑣 𝑖} 𝑛 𝑖 = 1$ defined by #m/def/linalg

⟨ 𝑣 𝑖, 𝑣 𝑗 ⟩ = 𝛿 𝑖 𝑗

Proof of existence and uniqueness

#missing/proof

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