[[Graded vector space]]
# Direct sum of graded vector spaces

The **direct sum** of $S$-[[Graded vector space|graded vector spaces]] $(V^i)_{i \in I}$ is the [[direct sum of vector spaces]] #m/def/linalg
$$
\begin{align*}
X = \bigoplus_{i \in I} V^i
\end{align*}
$$
with the [[Graded vector space|gradation]] $X = \bigoplus_{\alpha \in S} X_{\alpha}$ where
$$
\begin{align*}
X_{\alpha} = \bigoplus_{i \in I} V^i{}_{\alpha}
\end{align*}
$$
for $\alpha \in S$.


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