Let Q be 3 x 3 orthogonal matrix whose determinant is equal to 1 (a) If the eigenvalues of Q are all real and if they an ' ordered so that 1 2 3 deternine values of all possible triples of eigenvaIues (1 2, 3) (b) In the case that the eigenvalues 2 and 3 are complex what are the possible alues for ...

a Each eigenvalue has absolute value 1 and the product of the eigenvalues is eq ...

Let Q be 3 x 3 orthogonal matrix whose determinant is equal to 1. (a) If the

Question:

Let Q be 3 x 3 orthogonal matrix whose determinant is equal to 1.
(a) If the eigenvalues of Q are all real and if they an' ordered so that λ1 ≥ λ2 ≥ λ3. deternine values of all possible triples of eigenvaIues (λ1. λ2, λ3).
(b) In the case that the eigenvalues λ2 and λ3. are complex. what are the possible alues for λ1? Explain.
(c) Explain why λ = I must be an eigenvalue of Q.