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Linear Algebra

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Cauchy-Schwarz Equality Condition

LINALG-ZYXVE4

The Cauchy-Schwarz inequality gives a lower bound for the product $\lVert \vec v\rVert\lVert \vec w\rVert$ for any pair of vectors $\vec v,\vec w$.

Which condition on $\vec v,\vec w$ ensures that this lower bound is sharp (i.e., that the inequality is an equality)?

A

$\vec v$ and $\vec w$ are both unit vectors.

B

$\vec v$ and $\vec w$ are orthogonal.

C

$\langle \vec v,\vec w\rangle<0$

D

$\vec v$ and $\vec w$ are parallel.