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On a determinantal inequality arising from diffusion tensor imaging. (English) Zbl 1372.15019

In the paper under review, the following two determinantal inequalities are proved using the theory of majorization: \[ \det(A^2+\left|BA\right|^p)\leq\det(A^2+A^pB^p) \quad (0\leq p\leq2), \] and \[ \det(A^2+\left|AB\right|)\geq\det(A^2+AB). \] Motivated by the latter result, it is conjectured by the author that \[ \det(A^2+\left|AB\right|^p)\geq\det(A^2+A^pB^p)\quad (0\leq p\leq2). \]

MSC:

15A45 Miscellaneous inequalities involving matrices
15A15 Determinants, permanents, traces, other special matrix functions
15A60 Norms of matrices, numerical range, applications of functional analysis to matrix theory
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References:

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