Linear Algebra and Its Applications · Problem 6.4.11

Computations with Matrices — Gilbert Strang

Mathematics · rayleigh-quotient

Problem

Find the minimum values of

R(x) = \frac{x_1^2 - x_1 x_2 + x_2^2}{x_1^2 + x_2^2} \qquad \text{and} \qquad R(x) = \frac{x_1^2 - x_1 x_2 + x_2^2}{2x_1^2 + x_2^2}.