A unified framework for determinant dynamics under low-rank perturbations is developed that extends to singular matrices via pseudodeterminant and provides multiplicative decompositions for controllability Gramians.
Vrabel, A note on the matrix determinant lemma, International Journal of Pure and Applied Mathematics 111 (4) (2016) 643–646
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Determinant Dynamics under Low-Rank Perturbations: A Unified Framework for Singular Systems
A unified framework for determinant dynamics under low-rank perturbations is developed that extends to singular matrices via pseudodeterminant and provides multiplicative decompositions for controllability Gramians.