Ononot — For a symmetric matrix A with eigenvalues 0 < \lambda1 \leq

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Eigenvalues & Eigenvectorshard

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For a symmetric matrix $A$ with eigenvalues $0 < \lambda_1 \leq \lambda_2 \leq \cdots \leq \lambda_n$ , the Rayleigh quotient is $R(x) = \frac{x^T A x}{x^T x}$ . Which statement is true for any nonzero vector $x$ ?