- categories: Real Analysis, Theorem
Let be a normed vector space with an inner product . For all vectors , the Cauchy–Schwarz inequality states that:
where and are the norms of and , defined by:
Nov 14, 2024
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Jun 29, 20241 min read
Let V be a normed vector space with an inner product ⟨⋅,⋅⟩. For all vectors u,v∈V, the Cauchy–Schwarz inequality states that:
∣⟨u,v⟩∣≤∣∣u∣∣⋅∣∣v∣∣
where ∣∣u∣∣ and ∣∣v∣∣ are the norms of u and v, defined by:
∣∣u∣∣=⟨u,u⟩