Complexity of linear circuits and geometry

Fulvio Gesmundo; Jonathan Hauenstein; Christian Ikenmeyer; JM Landsberg

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arXiv · 1310.1362

Complexity of linear circuits and geometry

Fulvio Gesmundo·Jonathan Hauenstein·Christian Ikenmeyer·JM Landsberg

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Abstract

We use algebraic geometry to study matrix rigidity, and more generally, the complexity of computing a matrix-vector product, continuing a study initiated by Kumar, et. al. We (i) exhibit many non-obvious equations testing for (border) rigidity, (ii) compute degrees of varieties associated to rigidity, (iii) describe algebraic varieties associated to families of matrices that are expected to have super-linear rigidity, and (iv) prove results about the ideals and degrees of cones that are of interest in their own right.

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Fulvio Gesmundo, Jonathan Hauenstein, Christian Ikenmeyer, JM Landsberg. 2015-03-10. Complexity of linear circuits and geometry. https://arxiv.org/abs/1310.1362

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