Linear Algebra and Its Applications · Problem 6.1.16

Positive Definite Matrices — Gilbert Strang

Mathematics · positive-definite-matrices-tests-for-positive-definiteness

Problem

Show that f(x,y)=x2+4xy+3y2f(x,y) = x^2 + 4xy + 3y^2 does not have a minimum at (0,0)(0,0) even though it has positive coefficients. Write ff as a difference of squares and find a point (x,y)(x,y) where ff is negative.

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