Results 41 to 50 of about 2,856 (167)

Generalized Commutators and the Moore-Penrose Inverse

The Electronic Journal of Linear Algebra, 2021
This work studies the kernel of a linear operator associated with the generalized k-fold commutator. Given a set $\mathfrak{A}= \left\{ A_{1}, \ldots ,A_{k} \right\}$ of real $n \times n$ matrices, the commutator is denoted by$[A_{1}| \ldots |A_{k}]$. For a fixed set of matrices $\mathfrak{A}$ we introduce a multilinear skew-symmetric linear operator ...
openaire   +3 more sources

Determinantal Representations of Solutions and Hermitian Solutions to Some System of Two-Sided Quaternion Matrix Equations

Journal of Mathematics, 2018
Within the framework of the theory of quaternion row-column determinants previously introduced by the author, we derive determinantal representations (analogs of Cramer’s rule) of solutions and Hermitian solutions to the system of two-sided quaternion ...
Ivan I. Kyrchei
doaj   +1 more source

Moore–Penrose inverse of set inclusion matrices

, 2000
Given integers s,k and v, let Wsk be the vs×vk 0–1 matrix, the rows and the columns of which are indexed by the s-subsets and the k-subsets of a v-set respectively, and where the entry in row S and column U is 1 if S⊂U and 0 otherwise.
R.B. Bapat, Bapat, R. B., Bapat, R.B.
core   +1 more source

Line digraphs and the Moore-Penrose inverse

, 1981
Various characterizations of line digraphs and of Boolean matrices possessing a Moore-Penrose inverse are used to show that a square Boolean matrix has a Moore-Penrose inverse if and only if it is the adjacency matrix of a line digraph.
Per A. Smeds, Smeds, Per A.
core   +1 more source

The Moore–Penrose Inverse and Product Decomposition of Idempotent Operators on Hilbert C*-Modules

Axioms
We study the Moore–Penrose inverse of idempotent operators on Hilbert C*-modules. First, we extend the computation of the Moore–Penrose inverse of an idempotent operator and its difference from the range projection to this setting.
Wei Luo
doaj   +1 more source

Generalized inverses in graph theory

AKCE International Journal of Graphs and Combinatorics, 2023
–In this article, some interesting applications of generalized inverses in the graph theory are revisited. Interesting properties of generalized inverses are employed to make the proof of several known results simpler, and several techniques such as ...
Umashankara Kelathaya, Ravindra B. Bapat, Manjunatha Prasad Karantha   +2 more
doaj   +1 more source

Effective partitioning method for computing weighted Moore–Penrose inverse

, 2008
We introduce a method and an algorithm for computing the weighted Moore–Penrose inverse of multiple-variable polynomial matrix and the related algorithm which is appropriated for sparse polynomial matrices.
Petković, Marko D., Stanimirović, Predrag S., Tasić, Milan B.   +2 more
core   +1 more source

A Novel Parameter Estimation Method for Pneumatic Soft Hand Control Applying Logarithmic Decrement for Pseudo‐Rigid Body Modeling

Advanced Intelligent Systems, Volume 7, Issue 3, March 2025.
In this research, a paradigm of parameter estimation method for pneumatic soft hand control is proposed. The method includes the following: 1) sampling harmonic damping waves, 2) applying pseudo‐rigid body modeling and the logarithmic decrement method, and 3) deriving position and force control.
Haiyun Zhang, Kelvin HoLam Heung, Gabrielle J. Naquila, Ashwin Hingwe, Ashish D. Deshpande   +4 more
wiley   +1 more source

“It Is Much Safer to Be Sparse than Connected”: Safe Control of Robotic Swarm Density Dynamics with PDE Optimization with State Constraints

Advanced Intelligent Systems, EarlyView.
This paper proposes a novel control framework to ensure safety of a robotic swarm. A feedback optimization controller is capable of driving the swarm toward a target density while keeping risk‐zone exposure below a safety threshold. Theory and experiments show how safety is more effectively achieved for sparsely connected swarms.
Longchen Niu, Gennaro Notomista
wiley   +1 more source

Definition of Complex One-Parameter Generalized Moore–Penrose Inverses Using Differential Transformations

Computational and Mathematical Methods
This study presents analytical and numerical-analytical decomposition methods for determining complex one-parameter generalized inverse Moore–Penrose matrices. The analytical approach is based on the third Moore–Penrose condition, offering three solution
Sargis Simonyan, Hovhannes Abgaryan, Armine Avetisyan   +2 more
doaj   +1 more source