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[parent] zero vector space (Definition)

Definition A zero vector space is a vector space that contains only one element, a zero vector.

Properties

  1. Every vector space has a zero vector space as a vector subspace.
  2. A vector space $ X$ is a zero vector space if and only if the dimension of $ X$ is zero.
  3. Any linear map defined on a zero vector space is the zero map. If $ T$ is linear on $ \{0\}$, then $ T(0)=T(0\cdot 0) = 0T(0)=0$.



"zero vector space" is owned by drini. [ owner history (2) ]
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See Also: zero ring, zero map

Other names:  trivial vector space

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Cross-references: zero map, linear map, dimension, vector subspace, zero vector, contains, vector space
There are 7 references to this entry.

This is version 3 of zero vector space, born on 2003-10-31, modified 2004-02-13.
Object id is 5414, canonical name is ZeroVectorSpace.
Accessed 5304 times total.

Classification:
AMS MSC: 15-00 (Linear and multilinear algebra; matrix theory :: General reference works )
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