Category:Definitions/Quotient Norms
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This category contains definitions related to Quotient Norms.
Related results can be found in Category:Quotient Norms.
Let $X$ be a normed vector space.
Let $N$ be a closed linear subspace of $X$.
Let $X/N$ be the quotient vector space of $X$ modulo $N$.
Let $\pi : X \to X/N$ be the quotient mapping associated with $X/N$.
We define the quotient norm $\norm \cdot_{X/N}$ by:
- $\ds \norm {\map \pi x}_{X/N} = \inf_{z \in N} \norm {x - z}$
for each $x \in X$.
Pages in category "Definitions/Quotient Norms"
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