Computer Generation of Symbolic Generalized Inverses and Applications to Physics and Data Analysis
Problems in data analysis, electrical networks, and finite element methods often involve linear models having singular, square matrices or matrices which are not square. The concept of generalized inverse extends the ranges of application of the notion of matrix inverse to such matrices and provides powerful mathematical tools for handling them. The use of symbolic generalized inverses during the analyses of these problems is equally powerful but requires more manipulation than can be reasonably performed by a human analyst. In this paper, the symbolic calculation of the Moore-Penrose generalized inverse, based on Albert’s limit formulation, will be expressed in Macsyma and examples of its use will be given. In particular, the computer derivation of a novel form of the generalized inverse of a covariance matrix typically used in statistical analysis will be shown.
KeywordsGeneralize Inverse Roundoff Error Hand Calculation Algebraic Criterion Numerical Routine
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