| Line 2: | Line 2: | ||
* W contains the [[zero vector]] | * W contains the [[zero vector]] | ||
| − | * If two vectors u and v are in W, then | + | * If two vectors u and v are in W, then u+v must also be in W. (This is called "[[closed under addition]]") |
* If the vector v is in W, and k is some [[scalar]] (ie just some number), then kv must also be in W. (This is called "[[closed under scalar multiplication]]"). | * If the vector v is in W, and k is some [[scalar]] (ie just some number), then kv must also be in W. (This is called "[[closed under scalar multiplication]]"). | ||
Revision as of 07:01, 4 June 2009
A subset (call it W) of vectors is a subspace when it satisfies these conditions:
- W contains the zero vector
- If two vectors u and v are in W, then u+v must also be in W. (This is called "closed under addition")
- If the vector v is in W, and k is some scalar (ie just some number), then kv must also be in W. (This is called "closed under scalar multiplication").
Testing these conditions is the best way to see if it's a subspace.
