Results 41 to 50 of about 1,121,911 (166)

Ranks of a Constrained Hermitian Matrix Expression with Applications

Journal of Applied Mathematics, 2013
We establish the formulas of the maximal and minimal ranks of the quaternion Hermitian matrix expression C4−A4XA4∗ where X is a Hermitian solution to quaternion matrix equations A1X=C1, XB1=C2, and A3XA3*=C3.
Shao-Wen Yu
doaj   +1 more source

Structures preserved by generalized inversion and Schur complementation

Linear Algebra and its Applications, 2010
The authors investigate the inheritance of certain structures under generalized matrix inversion. These consist of rank and displacement structures. The study is done in such a way that the derivation of the preservation of rank structure can be carried over to that of the displacement structure.
Delvaux, Steven, Barel, Marc Van
openaire   +2 more sources

A note on the formulas for the Drazin inverse of the sum of two matrices

Open Mathematics, 2019
In this paper we derive the formula of (P + Q)D under the conditions Q(P + Q)P(P + Q) = 0, P(P + Q)P(P + Q) = 0 and QPQ2 = 0. Then, a corollary is given which satisfies the conditions (P + Q)P(P + Q) = 0 and QPQ2 = 0. Meanwhile, we show that the additive
Liu Xin, Yang Xiaoying, Wang Yaqiang
doaj   +1 more source

Generalization of the Sherman–Morrison–Woodbury formula involving the Schur complement [PDF]

Applied Mathematics and Computation, 2017
Let $X\in\mathbb{C}^{m\times m}$ and $Y\in\mathbb{C}^{n\times n}$ be nonsingular matrices, and let $N\in\mathbb{C}^{m\times n}$. Explicit expressions for the Moore-Penrose inverses of $M=XNY$ and a two-by-two block matrix, under appropriate conditions, have been established by Castro-González et al. [Linear Algebra Appl. 471 (2015) 353-368].
openaire   +3 more sources

Gap‐Free Information Transfer in 4D‐STEM via Fusion of Complementary Scattering Channels

Advanced Science, EarlyView.
Fused Full‐Field STEM (FF‐STEM) is introduced as a 4D‐STEM imaging modality that combines direct ptychography with tilt‐corrected dark‐field reconstruction in a single acquisition. Fourier‐space fusion using Wiener‐type spectral weighting closes the low‐frequency contrast gap inherent to bright‐field methods, delivering gap‐free, dose‐efficient, near ...
Shengbo You, Georgios Varnavides, Sagar Khavnekar, Nikita Palatkin, Sihan Shao, Mingjian Wu, Daniel Stroppa, Darya Chernikova, Baixu Zhu, Ricardo Egoavil, Stefano Vespucci, Dileep Krishnan, Xingchen Ye, Florian K. M. Schur, Erdmann Spiecker, Philipp Pelz   +15 more
wiley   +1 more source

On Schur complement of block diagonally dominant matrices [PDF]

, 2006
It is well-known that the Schur complements of strictly diagonally dominant matrices are strictly diagonally dominant [D. Carlson, T. Markham, Schur complements of diagonally dominant matrices, Czech. Math. J.
Zhang, Cheng-yi, Chen, Feng, Li, Yao-tang   +2 more
core   +1 more source

Linear Mechatronic Modeling of Rectangular Tank Sloshing Dynamics

International Journal of Mechanical System Dynamics, EarlyView.
ABSTRACT Sloshing dynamics in partially filled tanks can strongly influence system‐level behavior when fluid motion couples with rigid‐body dynamics. This paper presents a linear and acausal two‐dimensional sloshing model for rectangular tanks, based on the reformulation of established sloshing theory within a modular, multi‐domain modeling framework ...
Magnus Steinstø, Eilif Pedersen
wiley   +1 more source

Control Design Based on Generalized Lur'e Lyapunov Functions for Sampled‐Data Lur'e Systems

International Journal of Robust and Nonlinear Control, EarlyView.
ABSTRACT This article addresses the synthesis of stabilizing control laws for aperiodic sampled‐data Lur'e systems. Based on a hybrid system representation of the closed‐loop system and a timer‐dependent generalized Lur'e–Postnikov type Lyapunov function, stabilization conditions are obtained by separating decision variables with the application of two
Arthur Scolari Fagundes, João Manoel Gomes da Silva Jr., Sophie Tarbouriech   +2 more
wiley   +1 more source

Optimization Problems of Hermitian Quadratic Matrix-Valued Functions and Applications

Axioms
In this paper, we investigate optimization problems for a Hermitian quadratic matrix-valued function involving two variable matrices. We derive algebraic formulas for the maximal and minimal ranks and partial inertias of this function based on a ...
Sihem Guerarra
doaj   +1 more source

Initial State Privacy of Nonlinear Systems on Riemannian Manifolds

International Journal of Robust and Nonlinear Control, EarlyView.
ABSTRACT In this paper, we investigate initial state privacy protection for discrete‐time nonlinear closed systems. By capturing Riemannian geometric structures inherent in such privacy challenges, we refine the concept of differential privacy through the introduction of an initial state adjacency set based on Riemannian distances.
Le Liu, Yu Kawano, Antai Xie, Ming Cao
wiley   +1 more source