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单词 Cauchy–Schwarz inequality
释义
Cauchy–Schwarz inequality

Mathematics
  • In an inner product space V then |〈v,w〉| ≤ ∥v∥×∥w∥ for any v,wV, with equality if and only if v,w are linearly dependent. Thus, the angle between non-zero vectors v,w can be defined as arccos (〈v,w〉/(∥v∥×∥w∥)).


Statistics
  • If X and Y are two random variables thenCauchy–Schwarz inequalitywith equality if and only if P(aX = bY) = 1 for some real constants a and b, at least one of which is non-zero.


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