Is U+W the Same as U∪W in Vector Spaces?

[athrun200]

 

[CompuChip]

I know what $U \cup W$ is, but how is $U + W$ defined?

 

[athrun200]

I don't know, but I saw it from books

 

[Stephen Tashi]

There many different meanings for mathematical notations, depending on the context. The page you gave is not talking about "+" in the context of sets. (In the context of sets, some books use $A + B$ to denote $(A \cup B) - (A \cap B)$.)

The page is talking about vector spaces. In that contex, I think $U + W$ means the vector space consisting of all vectors $h$ that can be expressed as $h = u + w$ where $u \in U$ and $w \in W$.

However, if you want to be sure of the meaning of "+" in a particular book, you must see what that book says it means. There is no "universal" meaning for it.

 

[Deveno]

for vector spaces, particularly when U,W are subspaces of a vector space V,

U+W is a subspace of V, U∪W usually is not.