Linear Algebra and Its Applications · Problem 6.1.3

Positive Definite Matrices — Gilbert Strang

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

Problem

If a 2 by 2 symmetric matrix passes the tests

a > 0

ac > b^2

, solve the quadratic equation

\det(A - \lambda I) = 0

and show that both eigenvalues are positive.