very simple, change of basis.

• May 8th 2009, 12:12 AM
U-God
very simple, change of basis.
Considering the bases $S = (1,0),(0,1)$ and $B = (2,1),(3,2)$ find the transitition matrix $P_{S,B}$.

I know this is really simple, but I can never remember which way it is meant to go. Is $P_{S,B}$ the matrix that takes matrix $B$ to matrix $S$? or the other way around?
Seeing as S can be written as an identity matrix, the transition matrix taking S to B is just going to be B right?
Then to find the transition matrix to take B to S, I can jus take the inverse?

If you need to find the change-of-coordinate matrix from basis B to C, then the matrix $P_{C \longleftarrow B} = \left[ \left[\vec{b_{1}}\right]_{C} \left[ \vec{b_{2}}\right]_{C}\right]$