Thedifference between diagonalazation and basis transformation

why when we want to trasform a matrix to a diagonolized form
D=p^-1*A*P

but when we want to change a matrix to a new basis
[tex]
[A]_v=P*[A]_E*p^-1
[/tex]
??

why the transformation matrices are flipped??
 

HallsofIvy

Science Advisor
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They are not. It's just a different choice where which matrix is P and which is P-1.
 
but there is no choise
p is always a transformation matrix and P^-1 is its inverse

why the other formula flips them
??
 

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