When is B− A− a generalized inverse of AB?☆
Reads0
Chats0
TLDR
In this paper, it was shown that the generalized inverse of a matrix product can arise from factorizations of the matrix which is to be inverted, such as full rank factorizations, normal factorizations and singular value decompositions (SVD).About:
This article is published in Linear Algebra and its Applications.The article was published on 1994-10-01 and is currently open access. It has received 57 citations till now. The article focuses on the topics: Matrix (mathematics) & Generalized inverse.read more
Citations
More filters
Journal ArticleDOI
Moore–Penrose inverse in rings with involution
TL;DR: In this paper, the Moore-Penrose inverse (MP-inverse) was studied in the setting of rings with involution and the relation between regular, MP-invertible and well-supported elements was analyzed.
Journal ArticleDOI
Reverse order law for the Moore–Penrose inverse
TL;DR: In this paper, the reverse order law for the Moore-Penrose inverse of operators on Hilbert spaces is studied in the context of finite-dimensional settings. But it is not shown in this paper that the result can be extended to infinite dimensions.
Journal ArticleDOI
Inverse Order Rule for Weighted Generalized Inverse
Wenyu Sun,Yimin Wei +1 more
Abstract: The weighted generalized inverses have several important applications in researching the singular matrices, regularization methods for ill-posed problems, optimization problems, and statistics problems. In this paper we establish some sufficient and necessary conditions for inverse order rule of weighted generalized inverse.
Journal ArticleDOI
Further Results on the Reverse Order Law for Generalized Inverses
TL;DR: The reverse order rule $(AB)=B^\dag=B + A = A for the Moore-Penrose inverse is established in several equivalent forms.
Journal ArticleDOI
Reverse order laws in C∗-algebras☆
TL;DR: In this paper, the necessary and sufficient conditions for reverse order laws for generalized inverses in C ∗ -algebras, extending rank conditions for matrices and range conditions for Hilbert space operators, are given.
References
More filters
Book
Generalized inverses: theory and applications
Adi Ben-Israel,T. N. E. Greville +1 more
TL;DR: In this paper, the Moore of the Moore-Penrose Inverse is described as a generalized inverse of a linear operator between Hilbert spaces, and a spectral theory for rectangular matrices is proposed.
Journal ArticleDOI
Generalized Inverse of Matrices and Its Applications
TL;DR: In this article, the generalized inverse of matrices and its applications are discussed and discussed in terms of generalized inverse of matrix and its application in the context of generalization of matrix matrices.
Journal ArticleDOI
A Note on a Generalized Inverse of a Matrix with Applications to Problems in Mathematical Statistics
TL;DR: In this article, the author defined a pseudo inverse of a singular matrix and used it in representing a solution of normal equations and for obtaining variances and covariances of estimates in the theory of least squares.
Journal ArticleDOI
Generalized inverse of linear transformations: a geometric approach
C. Radhakrishna Rao,Haruo Yanai +1 more
TL;DR: The LM N-inverse as mentioned in this paper is a generalized inverse of a linear transformation A: →, where and are arbitrary finite dimensional vector spaces, defined using only geometrical concepts of linear transformations.