Linear Algebra and Its Applications · Problem 6.2.3

Positive Definite Matrices — Gilbert Strang

Mathematics · tests-for-positive-definiteness

Problem

Construct an indefinite matrix with its largest entries on the main diagonal: A=[1b−bb1b−bb1]with ∣b∣<1 can have det⁡A<0.A = \begin{bmatrix} 1 & b & -b \\ b & 1 & b \\ -b & b & 1 \end{bmatrix} \quad \text{with } |b| < 1 \text{ can have } \det A < 0.

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