If P is the transition matrix from basis B to basis B', what is the transition matrix from B' to B?
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The inverse of P
Transition matrices (or change-of-basis matrices) must be invertible because they represent a mapping between two different bases of the same vector space. Multiplying a coordinate vector by P transforms its representation from basis B to B'.
Also asked as:
- If P represents the change-of-basis matrix from B to B', what matrix represents the change from B' back to B?