Let Q be a 3 3 orthogonal matrix whose determinant is equal to 1. (a) If the eigenvalues
Chapter 6, Problem 23(choose chapter or problem)
Let Q be a 3 3 orthogonal matrix whose determinant is equal to 1. (a) If the eigenvalues of Q are all real and if they are ordered so that 1 2 3, determine the values of all possible triples of eigenvalues (1, 2, 3). (b) In the case that the eigenvalues 2 and 3 are complex, what are the possible values for 1? Explain. (c) Explain why = 1 must be an eigenvalue of Q. 2
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