Category:Quotient Metrics on Vector Spaces
Jump to navigation
Jump to search
This category contains results about Quotient Metrics on Vector Spaces.
Definitions specific to this category can be found in Definitions/Quotient Metrics on Vector Spaces.
Let $K$ be a field.
Let $X$ be a vector space over $K$.
Let $d$ be an invariant metric on $X$.
Let $N$ be a vector 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.
We define the quotient metric on $X/N$ induced by $d$ by:
- $\ds \map {d_N} {\map \pi x, \map \pi y} = \inf_{z \mathop \in N} \map d {x - y, z}$
for each $\map \pi x, \map \pi y \in X/N$.
Pages in category "Quotient Metrics on Vector Spaces"
The following 4 pages are in this category, out of 4 total.