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Solutions: An Inequality Involving Submatrices

95.1.1. An Inequality Involving Submatrices—Solutions. Two solutions have been proposed independently by Shuangzhe Liu (the poser of the problem) and by Jacob Goeree and Heinz Neudecker. Each of these solutions, which are published below, contains interesting derivations. 1. Solution —proposed by Shuangzhe Liu. The Cauchy and Kantorovich matrix inequalities assert that (see Marshall and Olkin, 1990)