Abstract: C.1 ▪ Definition of the Moore—Penrose generalized inverseAs is well known, for a nonsingular square matrix A ∊ ℂn×n, there is a unique matrix X ∊ ℂn×n, called the inverse of A and denoted A−1, such that XA = AX = In. The question arises as to whether the idea of an inverse matrix can be generalized to arbitrary matrices, whether square and singular or even rectangular. The answer to this question is yes, and several types of generalized inverses (or pseudo-inverses) have been proposed and studied in detail in the literature. See the books by Ben-Israel and Gre- ville [20], Campbell and Meyer [56], and Rao and Mitra [215], for example. Of these, the Moore-Penrose generalized inverse is one of the most widely used in applications, and we discuss it briefly here.
Publication Year: 2017
Publication Date: 2017-09-27
Language: en
Type: other
Indexed In: ['crossref']
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