(adsbygoogle = window.adsbygoogle || []).push({}); 1. Suppose that U is a subspace of V. What is U+U?

2. Relevant equations:

There's a theorem that states: Suppose that A and B are subspaces of V. Then V is the direct sum of A and B (written as A [plus with a circle around it] B) if and only if: 1) V=A+B (meaning, the two subspaces are technically able to be added), and 2) The intersection of A and B = {0}.

3. I don't understand what the addition symbol really means in this case... I know that addition of two subspaces is NOT the same as the union of two subspaces. The union of two subspaces of V is a subspace of V if and only if one of the subspaces is contained in the other. ...Help!

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# Homework Help: Linear Algebra - adding subspaces

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