Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Complexity of linear circuits and geometry   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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The categories of this paper are: math-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: bayes-an
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The categories of this paper are: adap-org
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The categories of this paper are: quant-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: acc-phys
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The categories of this paper are: nlin
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The categories of this paper are: nucl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: funct-an
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The categories of this paper are: solv-int
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The categories of this paper are: hep-th
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The categories of this paper are: gr-qc
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The categories of this paper are: supr-con
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The categories of this paper are: cmp-lg