# Category:Definitions/Quotient Vector Spaces

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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 2 subcategories, out of 2 total.

## Pages in category "Definitions/Quotient Vector Spaces"

The following 3 pages are in this category, out of 3 total.