The generalized Bott-Duffin inverse and its applications
TLDR
In this paper, the generalized Bott-Duffin inverse A (+) (L ) of A with respect to a subspace L is defined, and a unified treatment of a class of linear systems and extreme value problems with equality constraints is given.About:
This article is published in Linear Algebra and its Applications.The article was published on 1990-06-01 and is currently open access. It has received 57 citations till now. The article focuses on the topics: Generalized inverse & Subspace topology.read more
Citations
More filters
Journal ArticleDOI
A characterization and representation of the generalized inverse A(2)T,S and its applications
TL;DR: In this paper, an explicit expression for the generalized inverse A (2) T, S was presented, and the characterization, the representation theorem and the limiting process for A(2)T, S were established.
Journal ArticleDOI
Full-rank representation of generalized inverse AT,S(2) and its application
Xingping Sheng,Guoliang Chen +1 more
TL;DR: A full-rank representation of the generalized inverse A"T","S^(^2^) of a given complex matrix A, which is based on an arbitrary full-Rank decomposition of G, where G is a matrix such that R(T)=T and N(G)=S.
Journal ArticleDOI
A cramer rule for solution of the general restricted linear equation
TL;DR: For the unique solution or one of solutions of general restricted linear equations where A ∊ C m×n b∊ AT, and Tis an arbitrary but fixed subspace of Cn, a Cramer rule (determinantal formula) was derived in this paper.
Journal ArticleDOI
Representation and approximation of the outer inverse AT,S(2) of a matrix A
Yong-Lin Chen,Xin Chen +1 more
TL;DR: In this paper, the outer inverse A T,S (2) of a matrix A, which is the matrix X satisfying XAX=X, R(X), T and N(X)=S, was studied.
Journal ArticleDOI
Full-rank representations of outer inverses based on the QR decomposition
TL;DR: An efficient algorithm for computing A T, S ( 2 ) inverses of a given constant matrix A, based on the QR decomposition of an appropriate matrix W, is presented and relations between the derived representation of outer inverse and corresponding general representation based on arbitrary full-rank factorization are derived.
References
More filters
Book
Linear statistical inference and its applications
TL;DR: Algebra of Vectors and Matrices, Probability Theory, Tools and Techniques, and Continuous Probability Models.
Journal ArticleDOI
Linear Statistical Inference and its Applications
P. G. Moore,C. Radhakrishna Rao +1 more
TL;DR: The theory of least squares and analysis of variance has been studied in the literature for a long time, see as mentioned in this paper for a review of some of the most relevant works. But the main focus of this paper is on the analysis of variance.
Journal ArticleDOI
Linear Statistical Inference and Its Applications.
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.