Optimal ellipsoids and decomposition of positive definite matrices |
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| Authors: | Yuk J. Leung Rakesh |
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| Affiliation: | Department of Mathematical Sciences, University of Delaware, Newark, DE 19716, USA |
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| Abstract: | Given a positive definite matrix A, we characterize the unique diagonal matrix D, D?A, with the smallest determinant. Equivalently, given an ellipsoid A, we characterize the unique ellipsoid of the largest volume contained in A, with principal axes parallel to the coordinate axes. |
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| Keywords: | Ellipsoid Determinant maximization John's theorem |
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