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1

Definition of a vector space

A vector space is a set V equipped with the following data.

1. Addition operation
2. A zero vector
3. Scalar multiplication operation.

And it should satisfy the 8 rules

2

What do we need to do to prove a certain set can be give the structure of a vector space?

1. Define a set V
2. Define the data of an addition operation, a zero vector and a scalar multiplication operation
3. Then this data should satisfy the 8 rules

3

Definition of a Subspace

A subset U of a vector space V is called a subspace iff

For all u, u’EU, u + u’ E U
Zero vector is element of U
for all scalars k and all vectors u element of U, k*u is an element of U