Linear Algebra and Its Applications · Problem 6.2.41

Positive Definite Matrices — Gilbert Strang

Mathematics · tests-for-positive-definiteness

Problem

Find the eigenvalues and eigenvectors of Ax=λMxAx = \lambda Mx: [6−3−36]x=λ18[4114]x.\begin{bmatrix} 6 & -3 \\ -3 & 6 \end{bmatrix} x = \frac{\lambda}{18} \begin{bmatrix} 4 & 1 \\ 1 & 4 \end{bmatrix} x.

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