Is the adjoint of linear map only guaranteed to be equivalent to the conjugate transpose of the matrix when the matrix is taken with respect to an orthonormal basis? Is it sometimes still equivalent even when the basis is not orthonormal?(adsbygoogle = window.adsbygoogle || []).push({});

For the problem I'm working on, I have T(a+bx+cx^2)=bx, which is not self adjoint. Then the matrix wrt to the basis (1,x, x^2) is zero everywhere, but 1 in the second row, second column. The only explanation I can come up with for why it's matrix equals the conj. transpose of the matrix even though it is not self adjoint is that the basis is not orthonormal.

(sorry I don't know how to format things properly)

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# Adjoints & conj. transpose

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