Characterization of Jordan Vectors of Operator-Valued Functions with Applications in Differential Equations
DOI:
https://doi.org/10.5644/SJM.21.02.10Keywords:
Matrix Polynomials, Matrix rational functions, Eigenvalues, Generalized Jordan vectors, Operator functions, Root functionsAbstract
A well-known characterization of Jordan vectors of a matrix polynomial $L(z)$ is generalized to a characterization of Jordan vectors of the operator-valued function $Q(z)$ at an eigenvalue $\alpha \in \mathbb{C}$. The results are then applied to solve a system of nonlinear ordinary differential equations.
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