Category:Quotient Vector Space is Vector Space
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This category contains pages concerning Quotient Vector Space is Vector Space:
Let $K$ be a field.
Let $X$ be a vector space over $K$.
Let $N$ be a linear subspace of $X$.
Define:
- $X/N = \set {x + N : x \in X}$
where $x + N$ is the Minkowski sum of $x$ and $N$.
Define:
- $\paren {x + N} +_{X/N} \paren {y + N} = \paren {x + y} + N$
for $x, y \in X$, and:
- $\alpha \circ_{X/N} {x + N} = \paren {\alpha x} + N$
for $\alpha \in K$ and $x \in X$.
Then $\paren {X/N, +_{X/N}, \circ_{X/N} }_K$ is a vector space.
Pages in category "Quotient Vector Space is Vector Space"
The following 2 pages are in this category, out of 2 total.