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تسجيل مستخدم جديدAn extension of Harnack type determinantal inequality
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We revisit and comment on the Harnack type determinantal inequality for contractive matrices obtained by Tung in the nineteen sixtieth and give an extension of the inequality involving multiple positive semidefinite matrices.
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Let $A$ be a positive semidefinite $mtimes m$ block matrix with each block $n$-square, then the following determinantal inequality for partial traces holds [ (mathrm{tr} A)^{mn} - det(mathrm{tr}_2 A)^n ge bigl| det A - det(mathrm{tr}_1 A)^m bigr|, ]
where $mathrm{tr}_1$ and $mathrm{tr}_2$ stand for the first and second partial trace, respectively. This result improves a recent result of Lin [14].
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