Geodesic
A treatment of a determinant inequality of Fiedler and Markham
Czechoslovak Mathematical Journal, Tome 66 (2016) no. 3, pp. 737-742

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Fiedler and Markham (1994) proved $$ \Big (\frac {\mathop {\rm det } \widehat {H}}{k}\Big )^{ k}\ge \mathop {\rm det } H, $$ where $H=(H_{ij})_{i,j=1}^n$ is a positive semidefinite matrix partitioned into $n\times n$ blocks with each block $k\times k$ and $\widehat {H}=(\mathop {\rm tr} H_{ij})_{i,j=1}^n$. We revisit this inequality mainly using some terminology from quantum information theory. Analogous results are included. For example, under the same condition, we prove $$ \mathop {\rm det }(I_n+\widehat {H}) \ge \mathop {\rm det }(I_{nk}+kH)^{{1}/{k}}.$$
DOI : 10.1007/s10587-016-0289-3
Classification : 15A45
Keywords: determinant inequality; partial trace 
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     title = {A treatment of a determinant inequality of {Fiedler} and {Markham}},
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Lin, Minghua. A treatment of a determinant inequality of Fiedler and Markham. Czechoslovak Mathematical Journal, Tome 66 (2016) no. 3, pp. 737-742. doi: 10.1007/s10587-016-0289-3

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