Category:Definitions/Quotient Vector Spaces

From ProofWiki
Jump to navigation Jump to search

This category contains definitions related to quotient vector spaces.
Related results can be found in Category:Quotient Vector Spaces.


Let $V$ be a vector space.

Let $M$ be a vector subspace of $V$.


Then the quotient space of $V$ modulo $M$, denoted $V / M$, is defined as:

$\set {x + M : x \in X}$

where $x + M$ is the Minkowski sum of $x$ and $M$.



Furthermore, $V / M$ is considered to be endowed with the induced operations:

$\paren {x + M} + {y + M} := \paren {x + y} + M$
$\alpha \paren {x + M} := \alpha x + M$

Subcategories

This category has the following 3 subcategories, out of 3 total.

Pages in category "Definitions/Quotient Vector Spaces"

The following 4 pages are in this category, out of 4 total.