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A subset (call it W) of vectors is a subspace when it satisfies these conditions: | A subset (call it W) of vectors is a subspace when it satisfies these conditions: | ||
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*<math>{\mathbb R}^3</math> | *<math>{\mathbb R}^3</math> | ||
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[[Category:MA351]] | [[Category:MA351]] | ||
Revision as of 04:52, 18 August 2010
What is a "subspace" in linear algebra?
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 W is a subspace.
Some common subspaces of $ {\mathbb R}^3 $
- The zero vector, $ \vec 0 $
- A line running through the origin
- A plane passing through the origin
- $ {\mathbb R}^3 $
