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zero vector space
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(Definition)
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Definition A zero vector space is a vector space that contains only one element, a zero vector.
- Every vector space has a zero vector space as a vector subspace.
- A vector space $X$ is a zero vector space if and only if the dimension of $X$ is zero.
- Any linear map defined on a zero vector space is the zero map. If $T$ is linear on $\{0\}$ , then $T(0)=T(0\cdot 0) = 0T(0)=0$ .
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"zero vector space" is owned by drini. [ owner history (2) ]
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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 6988 times total.
Classification:
| AMS MSC: | 15-00 (Linear and multilinear algebra; matrix theory :: General reference works ) |
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