Is the trace of a matrix independent of basis?

[Trixie Mattel]

Hello,

Just wondering if the trace of a matrix is independent of basis, seeing as the trace of a matrix is equal to the sun of the eigenvalues of the operator that the matrix is a representation of.

Thank you

 

[mfb]

I think you answered your own question, but a quick look at Wikipedia would lead to the same result.

 

[Trixie Mattel]

I think you answered your own question, but a quick look at Wikipedia would lead to the same result.

Thank you mfb!

 

[PeroK]

Hello,

Just wondering if the trace of a matrix is independent of basis, seeing as the trace of a matrix is equal to the sun of the eigenvalues of the operator that the matrix is a representation of.

Thank you

What you might have meant is: if an operator is represented by a matrix $M_1$ in one basis, and $M_2$ in another basis, then is $Tr(M_1) = Tr(M_2)$?

There is an important point that an operator does not change by a change of basis, but the matrix representing an operator may change from basis to basis.