2 -6 -3 -6-3 2 -3 2 -6. The eigenvalues of the real symmetric matrix A are X₁ = 7 and A₂ = −7. Let A An orthonormal basis for the eigenspace for A₁ = 7 is B₁ {u₁} where 111 and an orthonormal basis for the eigenspace for A₂ = -7 is B₂ = {1₂, 13} where 112 Thus, if P= 113 then P is orthogonal and PT AP = D. and D

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