Conjugating by a change of coordinates matrix converts matrix representations with respect to different bases.

Created almost 9 years ago, updated about 8 hours ago

Let $A_B=[T]_B$, $A_C=[T]_C$, and $P=P_{B\leftarrow C}$ for an operator $T:V\to V$. Then $A_C=P^{-1}A_BP$. Thus different basis representations of one operator are similar. This is a coordinate change, not a change to the underlying operator.

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