Matu-Tarow Noda
Abstract
Generalized inverses have many applications in engineering problems, such as data analysis, electrical networks, character recognitions, and so on. The most frequently used generalized inverse is a Moore-Penrose type's one. Let A be m x n matrix. The Moore-Penrose generalized inverse of A, i.e., n x m matrix G, satisfies the following definitions:AGA = AGAG = G(AG)T = AG(GA)T = GAwhere I shows a unit matrix. The Moore-Penrose generalized inverse is uniquely determined for a given matrix A. We denote the Moore-Penrose generalized inverse of A as G = A+. Some properties of it are1. If A is regular, then A+ = A-12. If A = 0, then A+ = 03. If A is an m x n matrix and its rank is m, then A+ = AT(AAT)-1The problem is how to obtain G efficiently. Thus we wish to find a fast and stable method for the problem. The singular value decomposition (SVD) algorithm is well known numerical method which gives results quickly. However, on the accuracy of solutions, it is evident that an error-free method is preferable. Thus, here, we consider algebraic or symbolic methods for obtaining the Moore-Penrose generalized inverse.
Index Terms
- Algebraic methods for computing a generalized inverse
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