Linear Algebra and Its Applications · Problem 6.4.5

Computations with Matrices — Gilbert Strang

Mathematics · rayleigh-quotient

Problem

For any symmetric matrix AA, compute the ratio R(x)R(x) for the special choice x=(1,…,1)x = (1,\ldots,1). How is the sum of all entries aija_{ij} related to λ1\lambda_1 and λn\lambda_n?

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