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arXiv · 2108.05910

Monotonicity of the principal pivot transform

J. E. Pascoe·Ryan Tully-Doyle
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Abstract

We prove that the principal pivot transform (also known as the partial inverse, sweep operator, or exchange operator in various contexts) maps matrices with positive imaginary part to matrices with positive imaginary part. We show that the principal pivot transform is matrix monotone by establishing Hermitian square representations for the imaginary part and the derivative.

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J. E. Pascoe, Ryan Tully-Doyle. 2021-08-12. Monotonicity of the principal pivot transform. https://arxiv.org/abs/2108.05910

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