Results 11 to 20 of about 4,185 (184)
Numerical Range of Moore–Penrose Inverse Matrices
Mathematics, 2020 Let A be an n-by-n matrix. The numerical range of A is defined as W ( A ) = { x * A x : x ∈ C n , x * x = 1 } . The Moore–Penrose inverse A + of A is the unique matrix satisfying A A + A = A , A + A A + = A ...
Mao-Ting Chien
doaj +2 more sources
On matrix convexity of the Moore-Penrose inverse [PDF]
International Journal of Mathematics and Mathematical Sciences, 1996 Matrix convexity of the Moore-Penrose inverse was considered in the recent literature. Here we give some converse inequalities as well as further generalizations.
B. Mond, J. E. Pecaric
doaj +2 more sources
A Neural Network for Moore–Penrose Inverse of Time-Varying Complex-Valued Matrices
International Journal of Computational Intelligence Systems, 2020 The Moore–Penrose inverse of a matrix plays a very important role in practical applications. In general, it is not easy to immediately solve the Moore–Penrose inverse of a matrix, especially for solving the Moore–Penrose inverse of a complex-valued ...
Yiyuan Chai +4 more
doaj +1 more source
Convergence of Rump's method for computing the Moore-Penrose inverse [PDF]
, 2016 summary:We extend Rump's verified method (S. Oishi, K. Tanabe, T. Ogita, S. M. Rump (2007)) for computing the inverse of extremely ill-conditioned square matrices to computing the Moore-Penrose inverse of extremely ill-conditioned rectangular matrices ...
Chen, Yunkun, Wei, Yimin, Shi, Xinghua
core +1 more source
On the mean and variance of the estimated tangency portfolio weights for small samples
Modern Stochastics: Theory and Applications, 2022 In this paper, a sample estimator of the tangency portfolio (TP) weights is considered. The focus is on the situation where the number of observations is smaller than the number of assets in the portfolio and the returns are i.i.d.
Gustav Alfelt, Stepan Mazur
doaj +1 more source
Expressions and characterizations for the Moore-Penrose inverse
, 2023 Under certain conditions, we prove that the Moore-Penrose inverse of a sum of operators is the sum of the Moore-Penrose inverses. From this, we derive expressions and characterizations for the Moore-Penrose inverse of an operator that are useful for its ...
Patricia Morillas +2 more
core +1 more source
The dual index and dual core generalized inverse
Open Mathematics, 2023 In this article, we introduce the dual index and dual core generalized inverse (DCGI). By applying rank equation, generalized inverse, and matrix decomposition, we give several characterizations of the dual index when it is equal to 1. We realize that if
Wang Hongxing, Gao Ju
doaj +1 more source
Moore-Penrose inverse of some linear maps on infinite-dimensional vector spaces [PDF]
, 2020 [EN]The aim of this work is to characterize linear maps of infinite-dimensional inner product spaces where the Moore-Penrose inverse exists. This MP inverse generalizes the well-known Moore-Penrose inverse of a matrix A ∈ Mat _{n×m} (C).
Pablos Romo, Fernando +1 more
core +2 more sources
Idempotent operator and its applications in Schur complements on Hilbert C*-module
Special Matrices, 2023 The present study proves that TT is an idempotent operator if and only if R(I−T∗)⊕R(T)=X{\mathcal{ {\mathcal R} }}\left(I-{T}^{\ast })\oplus {\mathcal{ {\mathcal R} }}\left(T)={\mathcal{X}} and (T∗T)†=(T†)2T{\left({T}^{\ast }T)}^{\dagger }={\left({T ...
Karizaki Mehdi Mohammadzadeh +1 more
doaj +1 more source
Minimal Rank Properties of Outer Inverses with Prescribed Range and Null Space
Mathematics, 2023 The purpose of this paper is to investigate solvability of systems of constrained matrix equations in the form of constrained minimization problems.
Dijana Mosić +2 more
doaj +1 more source