# Thread: very simple, change of basis.

1. ## very simple, change of basis.

Considering the bases $\displaystyle S = (1,0),(0,1)$ and $\displaystyle B = (2,1),(3,2)$ find the transitition matrix $\displaystyle P_{S,B}$.

I know this is really simple, but I can never remember which way it is meant to go. Is $\displaystyle P_{S,B}$ the matrix that takes matrix $\displaystyle B$ to matrix $\displaystyle S$? 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?

2. This notation is really unstandardized, for instance, one of the texts i learned out of uses a lower and an upper script for the transition matrix from one basis to the other. You are going to have to look in the book or your teacher's notes to figure this one out I think.

If indeed it is talking about changing basis from the standard to B, then your analysis is correct, it is indeed just B.

3. hi

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

That is, the old basis expressed in terms of the new basis.
So the vectors in this matrix are the coordinate vectors of the B-vectors relative to the basis C.