Let {u1, u2, ... , un} be an orthonormal basis for Rn and let A be a linear combination
Chapter 6, Problem 30(choose chapter or problem)
Let {u1, u2, ... , un} be an orthonormal basis for Rn and let A be a linear combination of the rank 1 matrices u1uT 1 , u2uT 2 , ... , unuT n . If A = c1u1uT 1 + c2u2uT 2 ++ cnunuT n show that A is a symmetric matrix with eigenvalues c1, c2, ... , cn and that ui is an eigenvector belonging to ci for each i.
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