# How to take a complex conjugate of a 5*5 matrices?

#### qqchico

I'm doing a take home final and wanted reassurance that i'm doing the problem right. the question involves taking <Sz>of |psi>. I know it's
<psi|Sz|psi>. I've never done it for a spin 2 particle which is a 5*5 matrix.Do i just take the complex conjugate of the values without switching their position within the matrices.

#### Nylex

Ok, I don't really know what your notation means, but for any matrix, yeah, you just replace each element with its complex conjugate.

#### dextercioby

Homework Helper
"<psi|Sz|psi>" is not a 5*5 matrix,is just a number=matrix 1*1.If you mean

$$\langle\psi_{i}|\hat{S}_{z}|\psi_{j}\rangle \ , \ i,j=\overline{1,5}$$

,then yes,it's a complex matrix;unless $|\psi_{i}\rangle$ are eigenvectors of the selfadjoint operator $\hat{S}_{z}$,the entries in the matrix are complex #-s with nonzero imaginary part.

Daniel.

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