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→Trivial or zero vector space: A null space incidentally may or may not be 'the' zero space; but as concepts they indeed are different. |
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The simplest example of a vector space is the trivial one: {0}, which contains only the zero vector (see the third axiom in the [[Vector space]] article). 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-[[Dimension (vector space)|dimensional]] vector space over ''F''. Every vector space over ''F'' contains a [[Linear subspace|subspace]] [[isomorphic]] to this one.
The zero vector space is conceptually different from the [[null space]] of a linear operator ''L'', which is the [[Kernel (linear algebra)|kernel]] of ''L''. (Incidentally, the null space of ''L'' is a zero space if and only if ''L'' is [[injective]].)
==Field==
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