Question: Let A be a symmetric n à n matrix with eigenvalues λ1,..., λn. Show that there exists an orthonormal set of vectors {x1, ..., xn}

Let A be a symmetric n × n matrix with eigenvalues λ1,..., λn. Show that there exists an orthonormal set of vectors {x1, ..., xn} such that
x'Ax = E (x

for each x ˆˆ Rn.

x'Ax = E (x"x,) %3D i=1

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