A fundamental theorem on lambda-matrices with applications —I. Ordinary differential equations with constant coefficients

Abstract

The fundamental theorem of the title refers to a spectral resolution for the inverse of a lambda-matrix L(λ) = ∑ i=0 l A iλ i where the A i are n× n complex matrices and det A l ≠ 0. The idea of a Jordan normal form associated with such a lambda-matrixis developed in proving the theorem. Applications are made to the study of initial value problems and two-point boundary value problems for systems of constant-coefficient ordinary differential equations.