Linear Algebra and Its Applications · Problem 6.4.6

Computations with Matrices — Gilbert Strang

Mathematics · rayleigh-quotient

Problem

With

A = \begin{bmatrix} 2 & -1 \\ -1 & 2 \end{bmatrix}

, find a choice of

x

that gives a smaller

R(x)

than the bound

\lambda_1 \leq 2

that comes from the diagonal entries. What is the minimum value of

R(x)