Linear Algebra and Its Applications · Problem 6.2.35

Positive Definite Matrices — Gilbert Strang

Mathematics · tests-for-positive-definiteness

Problem

Use the pivots of A−12IA - \frac{1}{2}I to decide whether AA has an eigenvalue smaller than 12\frac{1}{2}: A−12I=[2.53039.57077.5].A - \frac{1}{2}I = \begin{bmatrix} 2.5 & 3 & 0 \\ 3 & 9.5 & 7 \\ 0 & 7 & 7.5 \end{bmatrix}.

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