Question: Let (u1. u2, . . . , un), be an orthonornial basis for Rn and let A be a linear combination of the rank I

Let (u1. u2, . . . , un), be an orthonornial basis for Rn and let A be a linear combination
of the rank I matrices u1uT1.u2uT2..... unun. If
A = cu;u+c2u2u++ C,u,u

how that A is a symmetric matrix with eigenvalues c1,c2 and that cn, is an eigenvector belonging to ci, for each i.

A = cu;u+c2u2u++ C,u,u

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