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- W4320165461 abstract "We prove the (generalized) principal pivot transform is matrix monotone, in the sense of the Lowner ordering, under minimal hypotheses. This improves on the recent results of J. E. Pascoe and R. Tully-Doyle, Monotonicity of the principal pivot transform, Linear Algebra Appl. 662 (2022) in two ways. First, we use the ``generalized principal pivot transform, where matrix inverses in the classical definition of the principal pivot transform are replaced with Moore-Penrose pseudoinverses. Second, the hypotheses on matrices for which monotonicity holds is relaxed and, in particular, we find the weakest hypotheses possible for which it can be true. We also prove the principal pivot transform is a matrix convex function on positive semi-definite matrices that have the same kernel (and, in particular, on positive definite matrices). Our proof is a corollary of a minimization variational principle for the principal pivot transform." @default.
- W4320165461 created "2023-02-13" @default.
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- W4320165461 date "2023-02-08" @default.
- W4320165461 modified "2023-09-29" @default.
- W4320165461 title "Matrix monotonicity and concavity of the principal pivot transform" @default.
- W4320165461 doi "https://doi.org/10.48550/arxiv.2302.04293" @default.
- W4320165461 hasPublicationYear "2023" @default.
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