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On the Computation of the Moore—Penrose Inverse of Matrices with Symbolic Elements

In: Statistical Inference, Econometric Analysis and Matrix Algebra

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  • Karsten Schmidt

    (Fakultält Wirtschaftswissenschaften)

Abstract

In this paper potential difficulties in using Greville's method for the computation of the Moore—Penrose inverse of a matrix that also contains symbolic elements are discussed. For the actual computation of the Moore—Penrose inverse of matrices whose elements are not numeric only, a Computer Algebra System has to be used. Initially, the computation of the Moore—Penrose inverse of a vector is considered which is a simple task if it only has numeric elements. If it contains symbolic elements, it might also be straightforward, but might turn out to be difficult. As Greville's method — an iterative algorithm that needs n steps for the computation of the Moore—Penrose inverse of an m by n matrix — requires the computation of the Moore—Penrose inverse of a vector in each step, the difficulty just mentioned might prevent the actual computation of the Moore—Penrose inverse of a matrix with symbolic elements.

Suggested Citation

  • Karsten Schmidt, 2009. "On the Computation of the Moore—Penrose Inverse of Matrices with Symbolic Elements," Springer Books, in: Bernhard Schipp & Walter Kräer (ed.), Statistical Inference, Econometric Analysis and Matrix Algebra, pages 349-358, Springer.
    • Handle: RePEc:spr:sprchp:978-3-7908-2121-5_24
    DOI: 10.1007/978-3-7908-2121-5_24
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