Linear Algebra and Its Applications · Problem 6.1.22

Positive Definite Matrices — Gilbert Strang

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

Problem

Which values of

c

give a bowl and which give a saddle point for the graph of

z = 4x^2 + 12xy + cy^2

? Describe this graph at the borderline value of

c