4.2
Vector Spaces
,Definition of a Vector Space
, Definition of a Vector Space (1 of 6)
Definition of a Vector Space
Let V be a set on which two operations (vector addition
and scalar multiplication) are defined. If the listed
axioms are satisfied for every u, v, and w in V and every
scalar (real number) c and d, then V is a vector space.
Addition:
1. u + v is in V. Closure under addition
2. u + v = v + u Commutative property
3. u + (v + w) = (u + v) + w Associative property
Vector Spaces
,Definition of a Vector Space
, Definition of a Vector Space (1 of 6)
Definition of a Vector Space
Let V be a set on which two operations (vector addition
and scalar multiplication) are defined. If the listed
axioms are satisfied for every u, v, and w in V and every
scalar (real number) c and d, then V is a vector space.
Addition:
1. u + v is in V. Closure under addition
2. u + v = v + u Commutative property
3. u + (v + w) = (u + v) + w Associative property
