Linear Algebra and Its Applications · Problem 6.1.6

Positive Definite Matrices — Gilbert Strang

Mathematics · positive-definite-matrices-minima-maxima-saddle-points

Problem

Suppose the positive coefficients

a

and

c

dominate

b

in the sense that

a + c > 2b

. Find an example that has

ac < b^2

, so the matrix is not positive definite.