[[Graded vector space]]
# Graded vector subspace

Let $V$ be an $S$-[[graded vector space]] over $\mathbb{K}$.
A [[Vector subspace|subspace]] $W \leq V$  is said to be **graded** iff $W = \bigoplus_{\alpha \in S} W_{\alpha}$ where $W_{\alpha} = W \cap V_{\alpha}$ for $\alpha \in S$. #m/def/linalg 
In this case one may construct the [[Quotient graded vector space]] so that it carries a natural $S$-gradation.
See [[Graded submodule]].


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#state/tidy | #lang/en | #SemBr