ellipsoid axis length

From: novis <standshik@xxxxxxxxx>
Date: Fri, 31 Aug 2007 11:59:17 -0700

hello all,
suppose {x: x'A^(-1)x=r^2} is an ellipsoid. we know that the principle
axes of the ellipsoid is given by the eigenvectors of A. Now how do we
show that radius along any particular axis is proportional to the
square root of the corresponding eigenvalue of A?
thanks

.

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