Further results on the Craig-Sakamoto equation
John Maroulas
TL;DR
This paper establishes necessary and sufficient conditions for the Craig-Sakamoto equation to hold universally and explores the spectral properties of matrices involved, advancing theoretical understanding in matrix analysis.
Contribution
It provides a complete characterization of when the Craig-Sakamoto equation holds and investigates related spectral properties, extending prior theoretical results.
Findings
Conditions for the Craig-Sakamoto equation to hold universally
Spectral properties of matrices A and B analyzed
Theoretical framework for matrix determinant identities
Abstract
In this paper necessary and sufficient conditions are stated for the Craig-Sakamoto equation det(I-sA-tB) = det(I-sA)det(I-tB), for all scalars s, t. Moreover, spectral properties for A and B are investigated.
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Taxonomy
TopicsMatrix Theory and Algorithms · Advanced Optimization Algorithms Research · Advanced Topics in Algebra