Basis is a set of n vectors that :
- are not linear combinations of each other (linearly independent)
- span the space (the space is then n-dimensional)
What does it mean for a vector b3 to be linearly independent to the vectors b1, b2
- b3 does not lie in the plane spanned by b1 and b2
b3 is not a1xb1 + b2xb2 for any a1 or a2.
- Changing basis means Changing the space.