Ononot — A 3 \times 3 real symmetric matrix A has eigenvalues \lambda

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Eigenvalues & Eigenvectorsmedium

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A $3 \times 3$ real symmetric matrix $A$ has eigenvalues $\lambda_1 = 2$ , $\lambda_2 = 5$ , $\lambda_3 = -1$ with corresponding orthonormal eigenvectors $u_1, u_2, u_3$ . The spectral decomposition of $A$ is: