Definition:Quotient Vector Space

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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:

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

Also see

  • Results about quotient vector spaces can be found here.