Please see the attached file for the full problem statement, and please show all steps in your solution.
Consider the Hermitian matrix
omega = 1/2
[2 0 0
0 3 -1
0 -1 3]
(1) Show that omega1 = omega2 = 1; omega3 = 2.
(2) Show that |omega = 2> is any vector of the form
1/((2a^2)^(1/2)) [0 a -a]
(3) Show that the omega = 1 eigenspace contains all vectors of the form
1/((b^2 + 2x^2)^(1/2)) [b c c]
either by feeding omega = 1 into the equations or by requiring that the omega = 1 eigenspace be orthogonal to |omega = 2>.© BrainMass Inc. brainmass.com December 24, 2021, 7:35 pm ad1c9bdddf
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The solution is attached below in two files that are identical in content; they differ only in format. The first is in MS Word format, while the other is in Adobe pdf format. Therefore, you can choose the format that is more suitable to you.
The characteristic polynomial of is:
The eigenvalues satisfy:
Thus we get:
So the eigenvalues are (with indices now assigned sequentially):
To find the ...
The solution describes how to find the eigenvalues and eigenvector of a 3 x 3 Hermitian matrix.