Linear Algebra and Its Applications · Problem 7.4.17

Linear Programming and Game Theory — Gilbert Strang

Mathematics · gershgorin-circles-examples

Problem

What bound on ∣λ∣max⁡|\lambda|_{\max} does Gershgorin give for these matrices (see Problem 4)? What are the three Gershgorin circles that contain all the eigenvalues? A=[.3.3.2.3.2.4.2.4.1]A=[2−10−12−10−12].A = \begin{bmatrix} .3 & .3 & .2 \\ .3 & .2 & .4 \\ .2 & .4 & .1 \end{bmatrix} \qquad A = \begin{bmatrix} 2 & -1 & 0 \\ -1 & 2 & -1 \\ 0 & -1 & 2 \end{bmatrix}.

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