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

David F. Delchamps
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David F. Delchamps: Cornell University, School of Electrical Engineering

Chapter 9 in State Space and Input-Output Linear Systems, 1998, pp 132-144 from Springer

Abstract: 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.

Date: 1998
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DOI: 10.1007/978-1-4612-3816-4_10

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