Linear Algebra and Its Applications · Problem 6.2.10

Positive Definite Matrices — Gilbert Strang

Mathematics · tests-for-positive-definiteness

Problem

The ellipse

u^2 + 4v^2 = 1

corresponds to

A = \begin{bmatrix} 1 & 0 \\ 0 & 4 \end{bmatrix}

. Write the eigenvalues and eigenvectors, and sketch the ellipse.