Algebraic Multiplicity Through Jordan Chains. Smith Form
This chapter studies the algebraic multiplicity according to the theory of Jordan chains. The concept of Jordan chain extends the classic concept of chain of generalized eigenvectors, already studied in Section 1.3. It will provide us with a further approach to the algebraic multiplicities χ and µ introduced and analyzed in Chapters 4 and 5, respectively, whose axiomatization has already been accomplished through the uniqueness theorems included in Chapter 6.
KeywordsBanach Space Open Neighborhood Operator Family Matrix Polynomial Continuous Family
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