Trying to find eigenvalues for this matrix
If my math is correct, the determinant of this is , but this doesn't factor, so I don't know how to find the roots.
Can somebody help? Thanks.
your math is incorrect.
the determinant is:
(1 - λ)^{3} - (-2)(-2)(1 - λ) - (2)(2)(1 - λ) = 1 - 3λ + 3λ^{2} - λ^{3} - 8(1 - λ) = -7 +5λ + 3λ^{2} - λ^{3}
this has one rational root, and two irrational roots which are "conjugate" (in the sense of square roots).