Examples of vector spaces: Difference between revisions

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The simplest example of a vector space is the trivial one: {'''0'''}, which contains only the zero vector (see axiom 3 of [[vector space]]s). Both vector addition and scalar multiplication are trivial. A [[basis (linear algebra)|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.

DoThe notzero confuse thisvector space withis different from the [[null space]] of a linear operator F, which is the kernel of F.

==Field==