So I understand that the change of basis of the matrix is $X' = U^{\dagger}XU$. But how about if I just want to change the basis of a vector $v$.

Is $v' = U^{\dagger}v$ the right one? Why does the $U$ disappear here?

  • $\begingroup$ You are using a lot of symbols without letting us know what any of them mean. $\endgroup$ – Gerry Myerson Sep 23 '16 at 7:18
  • $\begingroup$ related: math.stackexchange.com/questions/340978/change-of-basis-matrix $\endgroup$ – Ka-Wa Yip Sep 23 '16 at 7:33
  • $\begingroup$ Presumably $U$ is unitary and $\dagger$ is the adjoint. $\endgroup$ – Omnomnomnom Sep 23 '16 at 11:49
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    $\begingroup$ The key is to understand that $X'v'$ should produce the same result as $Xv$, but that output $Xv$ of $X$ should be expressed with respect to the new basis. $\endgroup$ – Omnomnomnom Sep 23 '16 at 11:53
  • $\begingroup$ @Omnomnomnom thank you. does that mean $v' = X'^{\dagger}Xv$? $\endgroup$ – Ka-Wa Yip Oct 6 '16 at 22:06

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