Minkowski inequality over complex positive definite matrices (Q2778637)

The author derives determinantal inequalities of the type NEWLINE\[NEWLINE |\det(A+B)|^{1/r} >|\det(A)|^{1/r}+|\det(B)|^{1/r} NEWLINE\]NEWLINE for complex positive definite matrices \(A, B\) and positive real numbers \(r,\) thus generalizing the Minkowski inequality. Moreover, these results are used to obtain further improvements of a number of other inequalities, e. g., the Ostrowski-Taussky inequality.