How Does the P-Transformation Matrix Convert Between Bases?

[transgalactic]

what is the right formula for the transformation of one base into
another ??

P-transformation matrix

is it S*A*S^-1

or

is it S^-1*A*S

 

[HallsofIvy]

That depends entirely upon what S is!

Obviously, if S*A*S^-1 goes from basis P to basis Q, S^-1*A*S goes from basis Q to basis P.