On the Relationship Between Real and Complex Linear Systems
Rings and Algebras
2017-06-02 v1 Numerical Analysis
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.
Cite
@article{arxiv.1706.00268,
title = {On the Relationship Between Real and Complex Linear Systems},
author = {Cédric Josz},
journal= {arXiv preprint arXiv:1706.00268},
year = {2017}
}