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Accepted
How to Verify the Conjugate transpose
Everything is ok. I've controlled all you calculations by Wolfram Alpha.
You can't easily use $\boxed{\langle A b_1, b_1 \rangle = \langle b_1, A^{*} b_1 \rangle}\color{red}*$ to check since $B \...
- 3,223
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How should we characterize the relationship between two matrix representations of a linear operator with respect to two different orthonormal bases?
I suspect this not what they are asking for. They probably want you to write an explicit equation relating the two matrices.
Since the matrices $A'$ and $A''$ represent the same operator in different ...
- 4,182
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How should we characterize the relationship between two matrix representations of a linear operator with respect to two different orthonormal bases?
I think the authors intended for you to express the elements in terms of each other. Currently, the relationship between the two expressions is still unclear. I would recommend using the closure ...
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If $U $ is a unitary linear operator, how can I show that any matrix representation of $U$ must be a unitary matrix?
All your restatements look correct and necessary to me.
To proceed further, use $\langle w|U|v\rangle^\ast=\langle v|U^\dagger|w\rangle$ (note $U^\dagger=U^{-1}$ when unitary) and
$$ |w_1\rangle\...
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