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On minimal factorizations of rational matrix functions

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Abstract

The theory of factorization of rational matrix functions W(λ) = = C(λI-A)−1B + D, as presented in the book Bart-Gohberg-Kaashoek [1], is extended here to the case where D = W(∞) is not invertible, and applied to factorizations of monic matrix polynomials.

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Bibliography

  1. 1.

    Bart, H., I. Gohberg, M.A. Kaashoek: Minimal Factorization of Matrix and Operator Functions. Operator Theory: Advances and Applications, Birkhäuser (1979).

  2. 2.

    Gohberg, I., P. Lancaster, L. Rodman: Spectral Analysis of matrix polynomials - 1. Canonical forms and divisors. Lin. Alg. and Appl. 20 (1978), 1–44.

  3. 3.

    Gohberg, I., P. Lancaster, L. Rodman: Representations and divisibility of operator polynomials. Can. J. Math. 30 (1978), 1045–1069.

  4. 4.

    Rosenbrock, H.: State-Space and Multivariable Theory. New-York, Wiley (1970).

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Cohen, N. On minimal factorizations of rational matrix functions. Integr equ oper theory 6, 647–671 (1983). https://doi.org/10.1007/BF01691919

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Keywords

  • Matrix Function
  • Rational Matrix
  • Matrix Polynomial
  • Minimal Factorization
  • Rational Matrix Function