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Register a new userOn 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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We present some new inequalities related to determinant and trace for positive semidefinite block matrices by using symmetric tensor product, which are extensions of Fiedler-Markhams inequality and Thompsons inequality.
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Olkin [3] obtained a neat upper bound for the determinant of a correlation matrix. In this note, we present an extension and improvement of his result.
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