Show that $V$ is the internal direct sum of the subspaces $A$ and $B$ $\iff$ every $v\in V$ can be written uniquely as $v = a+b$ where $a\in A, b\in B$.

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Exercise I.D.1

Show that $V$ is the internal direct sum of the subspaces $A$ and $B$ $\Leftrightarrow$ every $v \in V$ can be written uniquely as $v = a + b$ where $a \in A, b \in B$ .

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Follows directly from Proposition 13.

togrul.topal

2021-10-30 12:16

Exercise I.D.1

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