Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bilinear systems with two supports: Koszul resultant matrices,
  eigenvalues, and eigenvectors   A fundamental problem in computational algebraic geometry is the computation
of the resultant. A central question is when and how to compute it as the
determinant of a matrix. whose elements are the coefficients of the input
polynomials up-to sign. This problem is well understood for unmixed
multihomogeneous systems, that is for systems consisting of multihomogeneous
polynomials with the * 1 same support. However, little is known for mixed
systems, that is for systems consisting of polynomials with different supports.
We consider the computation of the multihomogeneous resultant of bilinear
systems involving two different supports. We present a constructive approach
that expresses the resultant as the exact determinant of a Koszul resultant
matrix, that is a matrix constructed from maps in the Koszul complex. We
exploit the resultant matrix to propose an algorithm to solve such systems. In
the process we extend the classical eigenvalues and eigenvectors criterion to a
more general setting. Our extension of the eigenvalues criterion applies to a
general class of matrices, including the Sylvester-type and the Koszul-type
ones.

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The categories of this paper are: comp-gas
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The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
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The categories of this paper are: stat
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The categories of this paper are: dg-ga
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The categories of this paper are: solv-int
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
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The categories of this paper are: eess
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The categories of this paper are: chem-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: econ
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The categories of this paper are: q-alg
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The categories of this paper are: q-bio
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The categories of this paper are: physics