Algebra and Geometry | Part IA, 2005

Let AA be a real 3×33 \times 3 symmetric matrix with eigenvalues λ1>λ2>λ3>0\lambda_{1}>\lambda_{2}>\lambda_{3}>0. Consider the surface SS in R3\mathbb{R}^{3} given by

xTAx=1x^{T} A x=1

Find the minimum distance between the origin and SS. How many points on SS realize this minimum distance? Justify your answer.

Typos? Please submit corrections to this page on GitHub.