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تسجيل مستخدم جديدOn a determinantal inequality arising from diffusion tensor imaging
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Minghua Lin
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In comparing geodesics induced by different metrics, Audenaert formulated the following determinantal inequality $$det(A^2+|BA|)le det(A^2+AB),$$ where $A, B$ are $ntimes n$ positive semidefinite matrices. We complement his result by proving $$det(A^2+|AB|)ge det(A^2+AB).$$ Our proofs feature the fruitful interplay between determinantal inequalities and majorization relations. Some related questions are mentioned.
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