Linear Algebra and Its Applications · Problem 6.2.2

Positive Definite Matrices — Gilbert Strang

Mathematics · tests-for-positive-definiteness

Problem

Decide for or against the positive definiteness of A=[2−1−1−12−1−1−12],B=[2−1−1−121−112],C=[012101210]2.A = \begin{bmatrix} 2 & -1 & -1 \\ -1 & 2 & -1 \\ -1 & -1 & 2 \end{bmatrix}, \quad B = \begin{bmatrix} 2 & -1 & -1 \\ -1 & 2 & 1 \\ -1 & 1 & 2 \end{bmatrix}, \quad C = \begin{bmatrix} 0 & 1 & 2 \\ 1 & 0 & 1 \\ 2 & 1 & 0 \end{bmatrix}^2.

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