Results 91 to 100 of about 949,602 (209)

The Moore-Penrose inverse over a commutative ring [PDF]

, 1992
Let R be a commutative ring with 1 and with an involution a → ā, and let MR be the category of finite matrices over R with the involution (aij) → (aij)∗ = (āji).
R.B. Bapat, Robinson, Donald W., Donald W. Robinson, Bapat, R. B., Bapat, R.B.   +4 more
core   +1 more source

The Moore-Penrose inverse of a morphism with factorization [PDF]

, 1981
Given an m-by-n matrix A of rank r over a field with an involutory automorphism, it is well known that A has a Moore-Penrose inverse if and only if rank A∗A=r= rank AA∗.
Puystjens, Roland, Robinson, Donald W.
core   +1 more source

Dykstra's Algorithm and a Representation of the Moore–Penrose Inverse

Journal of Approximation Theory, 2002
The convergence of Lardy's series representation of the Moore-Penrose inverse of a closed unbounded linear operator is proved via Dykstra's alternating projection algorithm.
openaire   +2 more sources

Approximating the Inverse of a Square Matrix with Application in Computation of the Moore-Penrose Inverse

Journal of Applied Mathematics, 2014
This paper presents a computational iterative method to find approximate inverses for the inverse of matrices. Analysis of convergence reveals that the method reaches ninth-order convergence.
F. Soleymani, M. Sharifi, S. Shateyi
doaj   +1 more source

On the Further Properties of the MPBT Inverse and Applications to Special Matrices

Mathematics
This paper aims to simplify the form of the MPBT inverse, further explore its properties, and discuss when it coincides with other generalized inverses. Notably, the MPBT inverse coincides with the Moore–Penrose inverse when the index of the matrix is at
Tingyu Zhao, Yuefeng Gao
doaj   +1 more source

Minors of the Moore-Penrose inverse

Linear Algebra and its Applications, 1993
The well-known Jacobi identity for the minors of an inverse matrix \(A^{-1}\) is generalized to the minors of the Moore-Penrose inverse \(A^ +\) of an arbitrary real \(m \times n\)-matrix \(A\) of rank \(r \geq 1\). As a consequence, conditions are given in the case \(m=n\), under which all principal minors of \(A^ +\) are nonnegative.
Miao, Jianming, Ben-Israel, Adi
openaire   +2 more sources

On the Sequential Composition of the Moore-Penrose Matrix Inverse

, 2023
<p>A technical note on the sequential compositionality of the Moore-Penrose Matrix Inverse.
Aziz, Benjamin
core   +1 more source

Some New Algebraic and Topological Properties of the Minkowski Inverse in the Minkowski Space

The Scientific World Journal, 2013
We introduce some new algebraic and topological properties of the Minkowski inverse A⊕ of an arbitrary matrix A∈Mm,n (including singular and rectangular) in a Minkowski space μ.
Hanifa Zekraoui, Zeyad Al-Zhour, Cenap Özel   +2 more
doaj   +1 more source

On the Moore-Penrose Inverse in C∗-algebras

, 2006
In this article, two results regarding the Moore-Penrose inverse in the frame of C*-algebras are considered. In first place, a characterization of the so-called reverse order law is given, which provides a solution of a problem posed by M. Mbekhta.
Enrico Boasso, Boasso, Enrico
core  

Least Squares Pure Imaginary Solution and Real Solution of the Quaternion Matrix Equation AXB+CXD=E with the Least Norm

Journal of Applied Mathematics, 2014
Using the Kronecker product of matrices, the Moore-Penrose generalized inverse, and the complex representation of quaternion matrices, we derive the expressions of least squares solution with the least norm, least squares pure imaginary solution with the
Shi-Fang Yuan
doaj   +1 more source