- #1

Austin Chang

- 38

- 0

**V**be a vector space. If U

_{1}and U

_{2}are subspaces of

**V**s.t. U

_{1}+U

_{2}=

**V**and U

_{1}and U

_{1}∩U

_{2}= {0

_{V}}, then we say that V is the internal direct sum of U

_{1}and U

_{2}. In this case we write V = U

_{1}⊕U

_{2}. Show that V is internal direct sum of U

_{1}and U

_{2}if and only if every vector in V may be written uniquely in the form v

_{1}+v

_{2}with v

_{1}∈U

_{1}and v

_{2}∈ U

_{2}.

What does it mean to be unique? Does it matter if it is unique?