(related to Definition: Subspace)
Please note that every vector space \(V\) over a given field \(F\) has two trivial subspaces:
\(U\) is sometimes also called the zero space. The vector \( 0_V \) has to exist, since \((V,\oplus)\) is a group, which is part of the definition of vector space. The index of the vector \(0_V\) is used to differentiate it from the zero element of the addition \(0\in F\), and can be omitted, if it is clear from the context, which zero element is meant.