For C = 2 0 0 1 and A = 1 1 1 1 , confirm that C TAC has eigenvalues of the same signs

Chapter 6, Problem 6.2.33

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For C = 2 0 0 1 and A = 1 1 1 1 , confirm that C TAC has eigenvalues of the same signs as A. Construct a chain of nonsingular matrices C(t) linking C to an orthogonal Q. Why is it impossible to construct a nonsingular chain linking C to the identity matrix?

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