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Merge pull request #6 from yallop/direct-sum
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Fix typos in definition of direct sum.
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zeramorphic authored Aug 5, 2023
2 parents ff2bfd2 + 97ab2c8 commit da24f74
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2 changes: 1 addition & 1 deletion ib/linalg/01_vector_spaces_and_linear_dependence.tex
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Expand Up @@ -384,7 +384,7 @@ \subsection{Dimensionality of sums}
\subsection{Direct sums}
\begin{definition}
Let \( V \) be an \( F \)-vector space and \( U, W \) be subspaces of \( V \).
We say that \( V = U \oplus V \), read as the direct sum of \( U \) and \( V \), if \( \forall v \in V, \exists!
We say that \( V = U \oplus W \), read as the direct sum of \( U \) and \( W \), if \( \forall v \in V, \exists!
u \in U, \exists!
w \in W, u + w = v \).
We say that \( W \) is \textit{a} direct complement of \( U \) in \( V \); there is no uniqueness of such a complement.
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