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1 results

  • 11 - Quasi-separable Moore−Penrose Inversion

  • from Part I - Lectures on Basics with Examples
  • Patrick Dewilde, Technische Universität München, Klaus Diepold, Technische Universität München, Alle-Jan Van der Veen, Technische Universiteit Delft, The Netherlands
  • Book:
    Time-Variant and Quasi-separable Systems
    Published online:
    24 October 2024
    Print publication:
    31 October 2024, pp 169-182

  • Summary

    This chapter considers the Moore–Penrose inversion of full matrices with quasi-separable specifications, that is, matrices that decompose into the sum of a block-lower triangular and a block-upper triangular matrix, whereby each has a state-space realization given. We show that the Moore–Penrose inverse of such a system has, again, a quasi-separable specification of the same order of complexity as the original and show how this representation can be recursively computed with three intertwined recursions. The procedure is illustrated on a 4 ? 4 (block) example.