-
A vector space
over a field consists of a set on which two operations and (respectively called vector addition and scalar multiplication) are defined so that and
such that the following axioms hold
such that such that
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(Friedberg 1.1) - If
such that , then -
(Friedberg 1.1.1) - The
vector is unique -
(Friedberg 1.1.2) - The additive inverse of
is unique. -
(Friedberg 1.2) In any vector space
, the following are true -
Let
be vector spaces. is isomorphic , denoted if there exists a Linear Transformation that is invertible. This linear transformation is an isomorphism from to . - (Friedberg 2.20) Let
be finite dimensional vector spaces. Then if and only if - (Friedberg 2.20.1 ) If
is a vector space over of dimension , then .
- (Friedberg 2.20) Let