Multi-attribute decision-making based on subjective and objective integrated eigenvector method

An integrated approach is proposed to investigate the fuzzy multi-attribute decision-making （MADM） problems, where subjective preferences are expressed by a pairwise comparison matrix on the relative weights of attributes and objective information is expressed by a decision matrix. An eigenvector method integrated the subjective fuzzy preference matrix and objective information is proposed. Two linear programming models based on subjective and objective information are introduced to assess the relative importance weights of attributes in an MADM problem. The simple additive weighting method is utilized to aggregate the decision information, and then all the alternatives are ranked. Finally, a numerical example is given to show the feasibility and effectiveness of the method. The result shows that it is easier than other methods of integrating subjective and objective information.

A Decorrelating DOA Estimation Based on the Principal Eigenvector for CDMA Frequency-Selective Fading Channels

A novel decorrelating DOA estimation algorithm of multipath signals for CDMA frequency selective fading channels based only on the principal eigenvector of its corresponding covariance matrix is proposed. The proposed algorithm has the advantages that the DOAs of the multipath signals can be estimated independently and all the other resolved multipath signal interference is eliminated. Simulation results show that this algorithm estimates the DOAs of multipath signals efficiently and accurately.

Symplectic eigenvector expansion theorem of a class of operator matrices arising from elasticity theory

This paper deals with the completeness of the eigenvector system of a class of operator matrices arising from elasticity theory, i.e., symplectic eigenvector expansion theorem. Under certain conditions, the symplectic orthogonality of eigenvectors of the operator matrix is demonstrated. Based on this, a necessary and sufficient condition for the completeness of the eigenvector system of the operator matrix is given. Furthermore, the obtained results are tested for the free vibration of rectangular thin plates.

COMPUTING THE EIGENVECTORS OF A MATRIX WITH MULTIPLEX EIGENVALUES BY SVD METHOD

Every matrix is similar to a matrix in Jordan canonical form,which has very important sense in the theory of linear algebra and its engineering application.For a matrix with multiplex eigenvalues,an algorithm based on the singular value decomposition(SVD) for computing its eigenvectors and Jordan canonical form was proposed.Numerical simulation shows that this algorithm has good effect in computing the eigenvectors and its Jordan canonical form of a matrix with multiplex eigenvalues.It is superior to MATLAB and MATHEMATICA.

Eigenvector Method for Ranking Alternatives with Vague Value Measurements

An eigenvector method for ranking alternatives whose measurements are given as vague values is provided. Firstly, a positive matrix is constructed which is defined as evaluation information matrix （EIM）. Based on four assumptions for evaluating alternatives, a ranking eigenvector is defined. And then it is proved, based on positive matrix theory, that the EIM＇s eigenvector corresponding to the maximal eigenvalue is the ranking vector. For alternatives whose characteristics are presented by vague sets, the proposed techniques can evaluate the degree of suitability to which an alternative satisfies the decision-maker＇ s requirement efficiently.

A FAMILY OF MODAL METHODS FOR COMPUTING EIGENVECTOR DERIVATIVES WITH REPEATED ROOTS

A family of modal methods for computing eigenvector derivatives with repeated roots are directly derived from the constraint generalized inverse technique which is originally formulated by Wang and Hu. Extensions are made to Akgun's method to allow treatment of eigensensitivity with repeated roots for general nondefective systems, and Bernard and Bronowicki's modal expansion approach is expanded to a family of modal methods.

Geography of Talent in China During 2000-2015:An Eigenvector Spatial Filtering Negative Binomial Approach

The increase in China’s skilled labor force has drawn much attention from policymakers,national and international firms and media.Understanding how educated talent locates and re-locates across the country can guide future policy discussions of equality,firm localization and service allocation.Prior studies have tended to adopt a static cross-national approach providing valuable insights into the relative importance of economic and amenity differentials driving the distribution of talent in China.Yet,few adopt longitudinal analysis to examine the temporal dynamics in the stregnth of existing associations.Recently released official statistical data now enables space-time analysis of the geographic distribution of talent and its determinants in China.Using four-year city-level data from national population censuses and 1%population sample surveys conducted every five years between 2000 and 2015,we examine the spatial patterns of talent across Chinese cities and their underpinning drivers evolve over time.Results reveal that the spatial distribution of talent in China is persistently unequal and spatially concentrated between 2000 and 2015.It also shows gradually strengthened and significantly positive spatial autocorrelation in the distribution of talent.An eigenvector spatial filtering negative binomial panel is employed to model the spatial determinants of talent distribution.Results indicate the influences of both economic opportunities and urban amenities,particularly urban public services and greening rate,on the distribution of talent.These results highlight that urban economic-and amenity-related factors have simultaneously driven China’s talent’s settlement patterns over the first fifteen years of the 21st century.

Derivatives of repeated eigenvalues and corresponding eigenvectors of damped systems

A procedure is presented for computing the derivatives of repeated eigenvalues and the corresponding eigenvectors of damped systems. The derivatives are calculated in terms of the eigenvalues and eigenvectors of the second-order system, and the use of rather undesirable state space representation is avoided. Hence the cost of computation is greatly reduced. The efficiency of the proposed procedure is illustrated by considering a 5-DOF non-proportionally damped system.

An enhanced method for estimating snow water equivalent in the central part of the Tibetan Plateau using raster segmentation and eigenvector spatial filtering regression model

Snow water equivalent(SWE)is an important factor reflecting the variability of snow.It is important to estimate SWE based on remote sensing data while taking spatial autocorrelation into account.Based on the segmentation method,the relationship between SWE and environmental factors in the central part of the Tibetan Plateau was explored using the eigenvector spatial filtering(ESF)regression model,and the influence of different factors on the SWE was explored.Three sizes of 16×16,24×24 and 32×32 were selected to segment raster datasets into blocks.The eigenvectors of the spatial adjacency matrix of the segmented size were selected to be added into the model as spatial factors,and the ESF regression model was constructed for each block in parallel.Results show that precipitation has a great influence on SWE,while surface temperature and NDVI have little influence.Air temperature,elevation and surface temperature have completely different effects in different areas.Compared with the ordinary least square(OLS)linear regression model,geographically weighted regression(GWR)model,spatial lag model(SLM)and spatial error model(SEM),ESF model can eliminate spatial autocorrelation with the highest accuracy.As the segmentation size increases,the complexity of ESF model increases,but the accuracy is improved.

Some ResuIts on the Principal Eigenvector

For a simple connected graph G, let A(G) and Q(G) be the adjacency matrix and signless Laplacian matrix, respectively of G. The principal eigenvector of A(G)(resp.Q(G)) is the unit positive eigenvector corresponding to the largest eigenvalue of A(G)(resp. Q(G)). In this paper, an upper bound and lower bound for the sum of the squares of the entries of the principal eigenvector of Q(G) corresponding to the vertices of an independent set are obtained.

Derivation of Floquet Eigenvectors Displacement for Optimal Design of LC Tank Pulsed Bias Oscillators

The paper presents an approximated and compact derivation of the mutual displacement of Floquet eigenvectors in a class of LC tank oscillators with time varying bias. In particular it refers to parallel tank oscillators of which the energy restoring can be modeled through a train of current pulses. Since Floquet eigenvectors are acknowledged to give a correct decomposition of noise perturbations along the stable orbit in oscillator's space state, an analytical and compact model of their displacement can provide useful criteria for designers. The goal is to show, in a simplified case, the achievement of oscillators design oriented by eigenvectors. To this aim, minimization conditions of the effect of stationary and time varying noise as well as the contribution of jitter noise introduced by driving electronics are deduced from analytical expression of eigenvectors displacement.

A Construction of Multi-Sender Authentication Codes from Eigenvalues and Eigenvectors of the Matrix Over Finite Fields

We construct one multi-sender authentication code by algebraic combination method from eigenvalues and eigenvectors of the matrix over nite elds. Some parameters and the probabilities of three kinds of successful attack of this code are also computed. For multi-sender authentication code,it allows a group of senders to construct an authenticated message for a receiver such that the receiver can verify authenticity of the received message.

EIGENVECTORS OF SYSTEM OF HAMMERSTEIN INTEGRAL EQUATIONS IN BANACH SPACES ANDAPPLICATIONS

In this paper, the author investigates the existence of eigenvectors of system of Hammerstein integral equations in Banach spaces by means of fixed point index theory. He also gives some applications to a system of S turm-Liouville problems of ordinary differential equations.

类星体中射电强度与Eigenvector 1的关系

为揭示射电强度R与Eigenvector1的联系,以SDSSDR7中的类星体源为母样本,通过限制基础物理参数黑洞质量和爱丁顿吸积率的范围选择研究样本,并根据射电强度R将样本分为不同的区间建立复合谱,用以探究Eigenvector1中典型观测参数随射电强度R的变化.结果表明:射电强度只与[OⅢ]线的强度正相关,而与光学FeⅡ线强度无关,说明射电辐射只是Eigenvector1中的二级过程,不是驱动因素.

Time Eigenvectors and Their Applications

Time eigenvectors and time operator are constructed from energy eigenvectors of system.Some features of them are described.Their applications to harmonic oscillating system and to double wave description of system are discussed.

Adaptive Generalized Eigenvector Estimating Algorithm for Hermitian Matrix Pencil

Generalized eigenvector plays an essential role in the signal processing field.In this paper,we present a novel neural network learning algorithm for estimating the generalized eigenvector of a Hermitian matrix pencil.Differently from some traditional algorithms,which need to select the proper values of learning rates before using,the proposed algorithm does not need a learning rate and is very suitable for real applications.Through analyzing all of the equilibrium points,it is proven that if and only if the weight vector of the neural network is equal to the generalized eigenvector corresponding to the largest generalized eigenvalue of a Hermitian matrix pencil,the proposed algorithm reaches to convergence status.By using the deterministic discretetime(DDT)method,some convergence conditions,which can be satisfied with probability 1,are also obtained to guarantee its convergence.Simulation results show that the proposed algorithm has a fast convergence speed and good numerical stability.The real application demonstrates its effectiveness in tracking the optimal vector of beamforming.

Eigenvectors of Permutation Matrices

The spectral properties of special matrices have been widely studied, because of their applications. We focus on permutation matrices over a finite field and, more concretely, we compute the minimal annihilating polynomial, and a set of linearly independent eigenvectors from the decomposition in disjoint cycles of the permutation naturally associated to the matrix.

Some Properties of Eigenvalues and Eigenvectors of Wilkinson Matrices

Some properties of characteristic polynomials, eigenvalues, and eigenvectors of the Wilkinson matrices W2n＋1 and W2n＋1 are presented. It is proved that the eigenvalues of W2n＋1 just are the eigenvalues of its leading principal submatrix Vn and a bordered matrix of Vn. Recurrence formula are given for the characteristic polynomial of W2＋n＋1 . The eigenvectors of W2＋n＋1 are proved to be symmetric or skew symmetric. For W2n＋1 , it is found that its eigenvalues are zero and the square roots of the eigenvalues of a bordered matrix of Vn2. And the eigenvectors of W2n＋1 , which the corresponding eigenvahies are opposite in pairs, have close relationship.

On Monotone Eigenvectors of a Max-<i>T </i>Fuzzy Matrix

The eigenvectors of a fuzzy matrix correspond to steady states of a complex discrete-events system, characterized by the given transition matrix and fuzzy state vectors. The descriptions of the eigenspace for matrices in the max-Lukasiewicz algebra, max-min algebra, max-nilpotent-min algebra, max-product algebra and max-drast algebra have been presented in previous papers. In this paper, we investigate the monotone eigenvectors in a max-T algebra, list some particular properties of the monotone eigenvectors in max-Lukasiewicz algebra, max-min algebra, max-nilpotent-min algebra, max-product algebra and max-drast algebra, respectively, and illustrate the relations among eigenspaces in these algebras by some examples.

Left Eigenvector of a Stochastic Matrix

We determine the left eigenvector of a stochastic matrix M associated to the eigenvalue 1 in the commutative and the noncommutative cases. In the commutative case, we see that the eigenvector associated to the eigenvalue 0 is (N1,Nn) , where Ni is the i–th iprincipal minor of N=M–In , where In is the identity matrix of dimension n. In the noncommutative case, this eigenvector is (P1-1,Pn-1) , where Pi is the sum in Q《αij》 of the corresponding labels of nonempty paths starting from i and not passing through i in the complete directed graph associated to M .