Results 21 to 30 of about 408 (148)
IEEE Access, 2019 Let G be a connected graph. The subdivision graph S(G) of a graph (G) is the graph obtained by inserting a new vertex into every edge of G. The set of such new vertices is denoted by I(G).
Qun Liu
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Linear Algebra and its Applications, 1979 AbstractLet A be an n×n complex matrix. For a suitable subspace M of Cn the Schur compression A M and the (generalized) Schur complement A/M are defined. If A is written in the form A= BCST according to the decomposition Cn=M⊕M⊥ and if B is invertible, then AM=BCSSB−1C and A/M=000T−SB−1C· The commutativity rule for Schur complements is proved: (A/M)/N=(
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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
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Some Results on the Drazin Inverse of a Modified Matrix with New Conditions
International Journal of Analysis and Applications, 2014 In this article, we consider representations of the Drazin inverse of a modified matrix M = A−CDdB with the generalized Schur complement Z = D − BAdC under different conditions given in recent articles on the subject.
Abdul Shakoor, Hu Yang, Ilyas Ali
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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
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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].
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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
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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 +15 more
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A Schur complement approach to a general extrapolation algorithm
Linear Algebra and its Applications, 2003 The authors use Schur complements and their properties to obtain various interpretations of the E-transformation. It is proved that ratios of determinants similar to those appearing in the E-transformation can be recursively computed by a triangular recursive scheme and that, reciprocally, quantities computed by such a scheme can be expressed as a ...
BREZINSKI C, REDIVO ZAGLIA, MICHELA
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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
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