Linear Algebra and Its Applications · Problem 6.2.11

Positive Definite Matrices — Gilbert Strang

Mathematics · tests-for-positive-definiteness

Problem

Reduce the equation 3u2−22 uv+2v2=13u^2 - 2\sqrt{2}\,uv + 2v^2 = 1 to a sum of squares by finding the eigenvalues of the corresponding AA, and sketch the ellipse.

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