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Homework Statement
The matrix A transforms space by rotating counterclockwise around z axis by ∏/4.
-What is A?
-Find a unit vector s.t. Au=u
(make sure the first nonzero is positive)
-for what λ's does Au = λu? write answer as a set {a,b,...}
Homework Equations
Unit vector u = x/norm(x)
The Attempt at a Solution
So I already found A :
[ sqrt2/2 -(sqrt2/2) 0
sqrt2/2 sqrt2/2 0
0 0 1]
which is correct.
How do I find u?
I think once I find u do I follow the process associated with finding eigenvalues
by using det(A-λI) to find λ's?