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arXiv · 1307.4272

The Nullity Theorem for Principal Pivot Transform

Robert Brijder
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Abstract

We generalize the nullity theorem of Gustafson [Linear Algebra Appl. (1984)] from matrix inversion to principal pivot transform. Several special cases of the obtained result are known in the literature, such as a result concerning local complementation on graphs. As an application, we show that a particular matrix polynomial, the so-called nullity polynomial, is invariant under principal pivot transform.

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Robert Brijder. 2013-09-17. The Nullity Theorem for Principal Pivot Transform. https://doi.org/10.1016/j.laa.2013.09.014

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