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The usual sum, which I know, of two vector spaces is a set which consists of all sums of the vectors. [tex]A+B=\{a+b|a\in A,\; b\in B\}[/tex]. Is this the same thing as the direct sum?

I think I saw somewhere (I don't remeber where) a definition, that a direct sum of two vector spaces is just a their union, where zeros are identified. Do I remember this wrong? In some places the direct sum is treated as a vector space, and the union doesn't produce a vector space, so I think that is wrong then...

The wikipedia seems to explain, the the direct sum of two vector spaces is merely their cartesian product, but if it is a cartesian product, why is it called a direct sum then?