Trivial or Zero Vector Space
The simplest example of a vector space is the trivial one: {0}, which contains only the zero vector (see axiom 3 of vector spaces). Both vector addition and scalar multiplication are trivial. A basis for this vector space is the empty set, so that {0} is the 0-dimensional vector space over F. Every vector space over F contains a subspace isomorphic to this one.
Do not confuse this space with the null space of a linear operator F, which is the kernel of F.
Read more about this topic: Examples Of Vector Spaces
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