Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Relationship Between Real and Complex Linear Systems   We consider the problem of solving a linear system of equations which
involves complex variables and their conjugates. We characterize when it
reduces to a complex linear system, that is, a system involving only complex
variables (and not their conjugates). In that case, we show how to construct
the complex linear system. Interestingly, this provides a new insight on the
relationship between real and complex linear systems. In particular, any real
symmetric linear system of equations can be solved via a complex linear system
of equations. Numerical illustrations are provided. The mathematics in this
manuscript constitute an exciting interplay between Schur's complement,
Cholesky's factorization, and Cauchy's interlace theorem.

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The categories of this paper are: mtrl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-lat
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The categories of this paper are: cmp-lg
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The categories of this paper are: physics
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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: nlin
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The categories of this paper are: cond-mat
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: adap-org