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About 10,000 papers for “Matrix function”

Function of a Matrix (pdf)

Gaillard, Pierre-Yves · Figshare · 2013

Let a be a square matrix with complex entries and f a function holomorphic on an open subset U of the complex plane. It is well known that f can be evaluated on a if the spectrum of a is contained in U. We show that, for a fixed f, the resulting matrix depends holomorphically on a. (This is a pdf file. Tex file: link below.)

Cited by 0Open access

Function Word Pearson Correlation Matrix.

James W. Pennebaker (487912), Cindy K. Chung (680871), Joey Frazee (680872) et al. · Figshare · 2015

<p><i>Note</i>. Preps. = prepositions. P.Pron. = personal pronouns. I.Pron. = impersonal pronouns. Aux. verbs = auxiliary verbs. Conjunc. = conjunctions. Negat. = negations. All correlations are statistically significant, p<.01, 25, 973 <i>df</i>.</p><p>Function Word Pearson Correlation Matrix.</p>

Cited by 0Open access

Function of a Matrix (pdf)

Pierre-Yves Gaillard · Figshare · 2013

Let a be a square matrix with complex entries and f a function holomorphic on an open subset U of the complex plane. It is well known that f can be evaluated on a if the spectrum of a is contained in U. We show that, for a fixed f, the resulting matrix depends holomorphically on a. (This is a pdf file. Tex file: link below.)

Cited by 0Open access

Organic Bi-Function Matrix Array

Yohsuke Matsushita, Hiroyuki Shimada, Takuya Miyashita et al. · 2004

We have proposed and demonstrated a bi-function matrix array (Bi-Matrix) with a stacked layer of organic electroluminescent device (OELD) and organic photodiode (OPD) matrix arrays. Independent operations of emission and photodetection can be achieved for the multilayered array, where, the maximum luminance of OELD was 1,290 cd/m2 and the ratio of photoconductivity to dark conductivity was 103. A prototype 4×4 Bi-Matrix was also demonstrated.

Cited by 0

Möbius function of matrix posets

Michal Medek · Digital Repository (National Repository of Grey Literature) · 2023

In this work, we focus on the M¨obius function µ(X, Y ) of four variants of containment posets of sparse matrices, for which the M¨obius function has not been studied before. A sparse matrix is a binary matrix containing at most one 1-cell in each row and column. We focus mainly on the dominated scattered containment, where X ≤ Y if X can be created from Y by removing some rows and columns and by changing some 1-cells to 0-cells. We consider this poset to be a generalization of the permutation poset, as for permutations σ and π, if σ ≤ π, then the permutation matrices Mσ and Mπ satisfy Mσ ≤ Mπ. For the dominated scattered containment, we study the values of the M¨obius function on intervals of the form [1, Y ], where 1 is the 1 × 1 matrix consisting of a single 1-cell. We show that the situation when Y contains a zero row or column can be reduced to a situation when Y has no such zero line, that is, Y is a permutation matrix. For a permutation matrix Y , we derived a theorem expressing µ(1, Y ) in terms of the blocks of the sum decomposition of Y .

Cited by 0

Function of a Matrix (pdf)

Pierre-Yves Gaillard · Figshare · 2013

Let a be a square matrix with complex entries and f a function holomorphic on an open subset U of the complex plane. It is well known that f can be evaluated on a if the spectrum of a is contained in U. We show that, for a fixed f, the resulting matrix depends holomorphically on a. (This is a pdf file. Tex file: link below.)

Cited by 0Open access

EQUIVARIANT MATRIX FUNCTION NEURAL NETWORKS

Batatia, I, Schaaf, LL, Csányi, G et al. · Apollo (University of Cambridge) · 2024

Graph Neural Networks (GNNs), especially message-passing neural networks (MPNNs), have emerged as powerful architectures for learning on graphs in diverse applications. However, MPNNs face challenges when modeling non-local interactions in graphs such as large conjugated molecules, and social networks due to oversmoothing and oversquashing. Although Spectral GNNs and traditional neural networks such as recurrent neural networks and transformers mitigate these challenges, they often lack generalizability, or fail to capture detailed structural relationships or symmetries in the data. To address these concerns, we introduce Matrix Function Neural Networks (MFNs), a novel architecture that parameterizes non-local interactions through analytic matrix equivariant functions. Employing resolvent expansions offers a straightforward implementation and the potential for linear scaling with system size. The MFN architecture achieves state-of-the-art performance in standard graph benchmarks, such as the ZINC and TU datasets, and is able to capture intricate non-local interactions in quantum systems, paving the way to new state-of-the-art force fields.

Cited by 0Open access

Transfer matrix and matrix Green function: the matching problem

H. Rodrı́guez-Coppola, V.R. Velasco, F. Garcı́a-Moliner et al. · Physica Scripta · 1990

The connection between the Green function and the transfer matrix is extended beyond the case of one single differential equation – e.g. a one band model. The Surface Green Function Matching analysis is thus performed in terms of transfer matrices when the Green functions involved are matrices. The practical use of the formalism is demonstrated by studying two physical problems. One is the spatial analysis of proximity effects associated with elementary excitations in a superconductor in contact with a normal metal or a different superconductor. The other one is a calculation of electronic states in semiconductor superlattices made of lead salts.

Cited by 7

The incomplete matrix beta function and its application to first Appell hypergeometric matrix function

Xuan Ma, Ahmed Bakhet, Fuli He et al. · Linear and Multilinear Algebra · 2023

In this paper, we first introduce the incomplete beta matrix function Bz(M,K),z∈C, for parameter matrices M and K in Cm×m using the neutrix limit and evaluation methods on their the partial derivatives. Also, we define a new extension of the Pochhammer matrix symbol in terms of the incomplete beta matrix functions. Furthermore, we then apply this extended matrix symbol for the incomplete first Appell hypergeometric matrix functions and obtain some of their properties.

Cited by 1

THE SMOOTHING FUNCTION OF THE NONSMOOTH MATRIX VALUED FUNCTION

Zhao Jinye · National University of Singapore · 2004

2004 This thesis is dedicated to my parentsAcknowledgements I would like to thank my advisor, Dr. Sun Defeng for all of his guidance, encouragement and support. He has inspired me through his own sincere interest in the areas of Operations Research. He taught me how to do research and did it well with great care and patience. I would also like to acknowledge National University of Singapore for providing me the financial support and the pleasant environment for my study. I am also grateful to many friends at National University of Singapore for their great help and support. Last but not least, I would like to thank my family. I am very thankful to my mother who has kept her very best for me. iii Contents

Cited by 3

Dirac Delta Function of Matrix Argument

Zhang, Lin · arXiv (Cornell University) · 2016

Dirac delta function of matrix argument is employed frequently in the development of diverse fields such as Random Matrix Theory, Quantum Information Theory, etc. The purpose of the article is pedagogical, it begins by recalling detailed knowledge about Heaviside unit step function and Dirac delta function. Then its extensions of Dirac delta function to vector spaces and matrix spaces are discussed systematically, respectively. The detailed and elementary proofs of these results are provided. Though we have not seen these results formulated in the literature, there certainly are predecessors. Applications are also mentioned.

Cited by 0Open access