Question 1161624: What are the four main things we need to define for a vector space?
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
1. A set of vectors over a field
2. The operation of vector addition and the set of vectors is closed over this operation. That is, if you add one vector to another, you get a vector that is in the same set.
3. The operation of scalar multiplication and the set of vectors is closed over this operation. If you multiply a field element by a vector element you get a vector in the set of vectors.
4. The operations adhere to the following axioms:
Associativity for addition, Commutativity for addition, an Identity Element for addition exists, an Inverse Element for addition exists, Compatibility of scalar and field multiplication [ab(v) = a(bv)], an Identity Element for scalar multiplication exists, Distributivity of scalar multiplication over vector addition, Distributivity of scalar multiplication wrt field addition.
John
My calculator said it, I believe it, that settles it
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