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Geometric multiplicity coincides with algebraic multiplicity

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Reference no: EM131587545

Question: Provide details for the proofs of Theorem.

Theorem: (a) All solutions of system (5.14.5) tend to zero as j → ∞ if and only if all eigenvalues of C have norm less than one.

(b) All solutions of system (5.14.5) are bounded if and only if all eigenvalues of C have norm less than or equal to one, and for those eigenvalues with norm one, the geometric multiplicity coincides with the algebraic multiplicity.

Reference no: EM131587545

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