Changing the reference frame
2018, Sep 23
Basis is a set of n vectors that :
 are not linear combinations of each other (linearly independent)
 span the space (the space is then ndimensional)
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.