Singular value decomposition of complexes
Danielle A. Brake, Jonathan D. Hauenstein, Frank-Olaf Schreyer, Andrew, J. Sommese, and Michael E. Stillman
TL;DR
This paper extends the concept of singular value decomposition from matrices to finite complexes of real vector spaces, providing methods for computation and exploring applications.
Contribution
It introduces a novel extension of SVD to complexes and offers two computational methods along with practical applications.
Findings
Two methods for computing SVD of complexes
Applications demonstrating the utility of the extended SVD
Theoretical framework for SVD of complexes
Abstract
Singular value decompositions of matrices are widely used in numerical linear algebra with many applications. In this paper, we extend the notion of singular value decompositions to finite complexes of real vector spaces. We provide two methods to compute them and present several applications.
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