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The M + N Decomposition for Matrices Which Are Not Semi-Simple

In: State Space and Input-Output Linear Systems

Author

Listed:
  • David F. Delchamps

    (Cornell University, School of Electrical Engineering)

Abstract

In this section, we continue the eigenvector/eigenvalue analysis of real (n × n) matrices A. We saw in §8how such an analysis leads not only to insights about the linear mappings A T: R n → R n and $$_A\hat T:{C^n} \to {C^n}$$ -C n → C n , but also to procedures which may, at least in principle, be used in computing (t–s)A and A (k–l) In the pages which follow, we focus attention on matrices A which are not semi-simple (hence, in particular, not diagonalizable); the techniques we shall be discussing should be viewed as generalizations of the techniques we employed in analyzing semi-simple A’s.

Suggested Citation

  • David F. Delchamps, 1998. "The M + N Decomposition for Matrices Which Are Not Semi-Simple," Springer Books, in: State Space and Input-Output Linear Systems, chapter 9, pages 132-144, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-3816-4_10
    DOI: 10.1007/978-1-4612-3816-4_10
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