Definition:Induced Norm

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Definition

Let $\struct {X, \norm {\, \cdot \,}_X}$ be a normed vector space.

Let $Y \subseteq X$ be a subspace.


Then the induced norm (on $Y$) is defined as the restriction of $\norm {\, \cdot \,}_X$ to $Y$.

$\norm {\, \cdot \,}_Y := \norm {\, \cdot \,}_X {\restriction_Y}$


Sources