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arXiv · 1706.00268

On the Relationship Between Real and Complex Linear Systems

Cédric Josz
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Abstract

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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Cédric Josz. 2017-05-26. On the Relationship Between Real and Complex Linear Systems. https://arxiv.org/abs/1706.00268

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