Linear Algebra and Its Applications · Problem 6.1.21

Positive Definite Matrices — Gilbert Strang

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

Problem

The graph of z=x2+y2z = x^2 + y^2 is a bowl opening upward. The graph of z=x2−y2z = x^2 - y^2 is a saddle. The graph of z=−x2−y2z = -x^2 - y^2 is a bowl opening downward. What is a test on F(x,y)F(x,y) to have a saddle at (0,0)(0,0)?

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