Changing the reference frame

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.