QM Measurement Problem: Expectation Value of Lz

[y.moghadamnia]

hi there,
I have been studying the postulates of QM in shankar book, and in the part it explains how measurement affects the system, it talks alittle about the expectation value and the uncertainty. then I came across this problem which I don't get. it gives three L(in x direcion), L(in y direction) and L(in z direction) matrices and then asks " take the state in which Lx=1. In this state what is the expectation value of Lz?" I don't understand this part:
how knowing Lx can help us calculate the expectation value of Lz?

 

[The_Duck]

Given the matrix that represents Lx, you can write down the unique vector (up to a phase factor) that is an eigenvector of Lx with eigenvalue 1. Then you can calculate the expectation of Lz for this eigenvector.

 

[y.moghadamnia]

aha, so that's the way u got to look at it. guess I should solve more problems to understand the way of looking at the problems.I asked people if they had good problems to send me but no one answered.