Let $A$ and $B$ be positive definite matrices and $S_{M}= \{x:x^TM^{-1}x \leq 1\}$ . Show that $S_{A} \subseteq S_{B}$ iff $B \succeq A$
How to prove $B-A \succeq 0 \Leftrightarrow$ ellipsoid $x^TBx \leq 1$ contains $x^TAx \leq 1$?