Higher-Order Singular-Value Derivatives of Rectangular Real Matrices
NeutralArtificial Intelligence
Higher-Order Singular-Value Derivatives of Rectangular Real Matrices
A new theoretical framework has been introduced for deriving higher-order Fréchet derivatives of singular values in real rectangular matrices. This approach utilizes reduced resolvent operators from Kato's analytic perturbation theory, which is significant because deriving closed-form expressions for these derivatives has been a complex challenge in matrix analysis. This advancement could enhance our understanding of matrix behavior and its applications in various fields, making it a noteworthy contribution to mathematical research.
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