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About
zero vector space
(Definition)
Definition
A
zero vector space
is a
vector space
that
contains
only one element, a
zero vector
.
Properties
Every vector space has a zero vector space as a
vector subspace
.
A vector space
is a zero vector space if and only if the
dimension
of
is zero.
Any
linear map
defined on a zero vector space is the
zero map
. If
is linear on
, then
.
"zero vector space" is owned by
drini
.
[
owner history
(2) ]
(
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)
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See Also:
zero ring
,
zero map
Other names:
trivial vector space
This object's
parent
.
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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 )
Pending Errata and Addenda
None.
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