Thedifference between diagonalazation and basis transformation

why when we want to trasform a matrix to a diagonolized form

but when we want to change a matrix to a new basis

why the transformation matrices are flipped??


Science Advisor
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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