Commentary on "Toward a Noncommutative Arithmetic-geometric Mean Inequality: Conjectures, Case-studies, and Consequences"
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چکیده
In their paper, Recht and Ré have presented conjectures and consequences of noncommutative variants of the arithmetic mean-geometric mean (AM-GM) inequality for positive definite matrices. Let A1, . . . , An be a collection of positive semidefinite matrices and i1, . . . , ik be random indices in {1, . . . , n}. To avoid symmetrization issues that arise since matrix products are non-commutative, Recht and Ré define the expectation operators
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تاریخ انتشار 2012