Operator in three level system -- Eigenvalues/Eigenvectors

[jmgddg]

There is an operator in a three-state system given by:

2 0 0
A_hat = 0 0 i
0 -i 0

a) Find the eigenvalues and Eigenvectors of the operator
b) Find the Matrix elements of A_hat in the basis of the eigenvectors of B_hat
c) Find the Matrix Elements of A_hat in the basis vectors given by

1 0 0
|e1) = 0 , |e2) = 1 , |e3) = 0
0 0 1

 

[MichPod]

$300 and I can solve this.

 

[PeterDonis]

Moderator's note: Moved to homework forum.

 

[jmgddg]

Something went wrong with the formatting but the operator is
2,0,0
0,0,i
0,-i,0

And the 3 vectors respectively are
1
0
0

0
1
0

0
0
1​