Linear Algebra and Its Applications · Problem 6.2.38

Positive Definite Matrices — Gilbert Strang

Mathematics · tests-for-positive-definiteness

Problem

Find by experiment the number of positive, negative, and zero eigenvalues of

A = \begin{bmatrix} I & B \\ B^T & 0 \end{bmatrix}

when the block

B

(of order

\frac{1}{2}n

) is nonsingular.