Linear Algebra and Its Applications · Problem 6.1.1

Positive Definite Matrices — Gilbert Strang

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

Problem

The quadratic

f = x^2 + 4xy + 2y^2

has a saddle point at the origin, despite the fact that its coefficients are positive. Write

f

as a difference of two squares.