Normal operators and self adjointness

[evilpostingmong]

But I guess if T=UDU^(-1) and U is unitary, then T=D. So
T^2=(UDU^(-1))^2=D^2. If D^2=D, then T^2=T.

 

[Dick]

No T isn't equal to D. U represents the transformation to the basis where T is represented by the diagonal matrix D.

 

[evilpostingmong]

No T isn't equal to D. U represents the transformation to the basis where T is represented by the diagonal matrix D.

Oh so you mean U transforms D into a matrix that represents the basis where D came from, right?
Or is it that U transforms D into a matrix that represents T?

 

[Dick]

Both basically. U does one, U^(-1) does the other.