Discuss the below:
Q: Consider the Hermitian matrix
ω = 1/2
[2 0 0
0 3 -1
0 -1 3]
(1) Show that ω1 = ω2 = 1; ω3 = 2.
(2) Show that |ω = 2> is any vector of the form
1/((2a^2)^(1/2)) [0 a -a]
(3) Show that the ω = 1 eigenspace contains all vectors of the form
1/((b^2 + 2x^2)^(1/2)) [b c c]
either by feeding ω= 1 into the equations or by requiring that the omega = 1 eigenspace be orthogonal to |ω = 2>.