Matrix Transformation of operator from basis B' to B

1. The problem statement, all variables and given/known data



Hi guys, actually this isn't a homework question, but rather part of the working in a textbook on Linear Algebra.







2. Relevant equations







3. The attempt at a solution



I'm not sure why it's U*_li instead of U*_il. Shouldn't you flip the order when you do a matrix transpose?

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