We study the Legendre ellipsoid and the LYZ ellipsoid.First,we give a direct proof of the Cramer-Rao inequality for convex bodies.Second,we prove that origin-centered ellipsoids are the only convex bodies with identic...We study the Legendre ellipsoid and the LYZ ellipsoid.First,we give a direct proof of the Cramer-Rao inequality for convex bodies.Second,we prove that origin-centered ellipsoids are the only convex bodies with identical Löwner and Legendre ellipsoids.Finally,we establish a mean width inequality for convex bodies whose LYZ ellipsoids are the Euclidean unit ball.展开更多
文摘We study the Legendre ellipsoid and the LYZ ellipsoid.First,we give a direct proof of the Cramer-Rao inequality for convex bodies.Second,we prove that origin-centered ellipsoids are the only convex bodies with identical Löwner and Legendre ellipsoids.Finally,we establish a mean width inequality for convex bodies whose LYZ ellipsoids are the Euclidean unit ball.
