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Properties of Linear Systems
Existence of Solutions of the VectorMatrix Equation dydt Aty
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Applying approaches zero assume asymptotic behavior asymptotic development asymptotic expansion asymptotic form asymptotic series boundedness change of variable Chap chapter coefficients components condition Consequently Consider the equation constant matrix continuous contradiction converges uniformly curve derive diagonal difference equation discussion distinct characteristic roots du/dt dz/dt Exercise follows function Furthermore Hardy's theorem Hence implies inequality infinitely integral equation intersection interval Lemma Let us show linear differential equations linear equation linear systems linearly independent Math method of successive monotone increasing multiple characteristic roots nonsingular nonsingular matrix norm null vector obtain oscillatory periodic matrix positive proper solution possesses proof properties prove rational function result Riccati equation satisfies scalar second-order sequence solution of dy/dt stability successive approximations sufficiently small t'un tion transformation uniform convergence vector whence Wronskian yields yk(s yk(t zn+i