**Eigen** value, or characteristic value, problems are a special case of boundary value problems that are common in engineering problems contexts involving vibrations, elasticity and other oscillating systems. A wide variety of methods are available for solving **Eigen** value problems. Most are based on two step process. The first step involves transforming the original matrix to simpler one that retains all the original **Eigen** **values**. Then iterative methods are used to determine these **Eigen** **values**. Jacobi method, Given’s method and Householder method are used to find **Eigen** **values** of symmetric matrix. Aside from symmetric matrix, LR and QR method are used to find **Eigen** **values** of non symmetric matrices. This paper discusses the ccomparison of the speed and accuracy of these methods. The results of this study indicate that the QR algorithm is more successful method for finding the **Eigen** **values** of a real non symmetric matrix.

showed the **eigen** **values** for each letter no. of rows in matrix refers to no. of parts in thinned image and no. of column refers to no. of neighbors for each part . The operation of portioning thinned image is based on topology features . In next experiment two images for different letters are tested that they have same size and same font , **eigen** **values** computed for two images. See below in figure (2) :-

Abstract: - Decomposing the complete fuzzy graph into Hamiltonian fuzzy cycles is called the Hamiltonian fuzzy decomposition. The complete fuzzy graph of (2n+1) vertices can be decomposed into n Hamiltonian fuzzy cycles and the complete fuzzy graph of 2n vertices can be decomposed into (n-1) Hamiltonian fuzzy cycles. In this paper we discuss about, which one of these Hamiltonian fuzzy cycles having the shortest distance by using the **Eigen** **values**. Keywords: - Complete fuzzy graph, Covariance matrix, **Eigen** value, Fuzzy graph, Hamiltonian fuzzy cycle.

The natural fundamental frequencies of the structure / component can be determined using classical methods as well as using finite element technique which is widely reported in the literature. It is well known that the numerical analysis results are valid only for particular **values** of the parameters considered in the analysis. The structural engineers concerned with dynamic analysis or design of structures need a design formula or program for rapid determination of the governing natural frequency. The numerical **values** obtained by running the program are quite gratifying with those reported in literature[16] and reproduced in Table 1.

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and its isotopes. The **eigen** **values** and **eigen** vectors of the host system are computed using a Born-von Karman formalism. The mean square displacements of hydrogen isotope and its surrounding host crystal atoms are computed using scattering matrix formalism and green function method. Diffusion parameters of hydrogen isotopes are estimated using reaction coordinate approach incorporating the scattering matrix formalism and green function technique. The theoretically calculated results are comparable with the existing experimental results. Keywords: HfTi 2 , **eigen** **values**, **eigen** vectors,

Figure 2 and Figure 3 show the dependence of the real (a) and imaginary (b) parts of the eigenvalues of the spectral problem (9), (18) the parameter α and n = 0.4 respectively. The numbers marked on the charts num- ber of oscillations in the ascending order of the real part of the **Eigen** **values**. In all cases, except for the first mode and the second mode (n = 4) for the real parts of these curves have the form of smooth decreasing steps with a maximum angle of inclination of the tangent to the segment α ∈ [ 0.85;1.0 ] corresponding imaginary parts have a characteristic maximum.

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In engineering, **Eigen** value problems are commonly encountered. Since there is heavy demand for solving complicated problems, research in area of Numerical linear algebra is very active which is associated with stability and perturbation analysis for practical application. In recent year, a number of method have been proposed for finding **Eigen** **values** such as Power, Lanczos, Jacobi, Rutishauser etc. The work of H. Rutishauser proved to be fundamental in many areas of numerical analysis, especially, algorithms for solving **Eigen** value problems. The method of Lanczos has become one of the most successful methods for approximating a few **Eigen** **values** of a real symmetric matrix. In this paper the existing method available has been explained, where the original matrix is reduced to a tridiagonal matrix whose **Eigen** **values** are same as those of original matrix. The intention of this paper is just to review the methods and give step by step procedure to compute **Eigen** **values**.

Graph theory has been widely used for synthesis and analysis of the Planetary Gear Trains (PGTs). For analysis and synthesis of PGTs, many approaches were introduced by various kinematicians. Identifying the isomorphism for a given number of PGTs generated is the one of the challenging problem in structural synthesis to avoid the duplicate graphs. Different kinematicians [1-24] used adjacency [3], distance [4], flow [5], joint-joint [6] matrices etc to represent graphs of PGTs for analysis and synthesis. Characteristic polynomial [4], random number technique [7], Max code [8], Min code [9], Identification code [10], link path code [11], **Eigen** **values** and **Eigen** vectors [12-14], genetic algorithm [15], fuzzy logic [16], Hamming Number Technique [17] and loop based hamming [18] etc are the methods used to detect the isomorphism in kinematic chains and PGTs. Each and every method has its own merits and demerits. Most of the above methods are based on adjacency matrix of a PGT. Techniques for identifying the kinematic structure of the PGTs are given by two main criteria’s namely graphical method and Numerical method. Graphical methods are based on visual inspection of schematic diagrams of a PGT and many of the numerical methods are based on theory of graphs.

parameters were supposed to be equal to zero. Further with these numerical **values** of the parameters, the diagonalization of the second rank matrix was done, from where the calculated energies (**eigen** **values**) and coupling coefficients (**eigen** vectors) were obtained. Knowing the latter from (11) one determines the numerical **values** of the elements of second rank no diagonal matrices С 1 , С 4 , С 5 .

The **values** of characteristic polynomial coefficients are invariants for a [JJ] matrix. To make these [JJ] matrix characteristic polynomial coefficients as a powerful single number characteristic index, new composite invariants have been proposed. These invariants are ‘SCPC’ and ‘MCPC’. These invariants are unique for a [JJ] matrix and may be used as identification numbers to detect the isomorphism among simple jointed kinematic chains. The characteristic polynomial coefficients **values** are the characteristic invariants for the kinematic chains. Many investigators have reported co-spectral graph (non-isomorphic graph having same **Eigen** spectrum). But these **Eigen** spectra (**Eigen** **values** or characteristic polynomial) have been determined from (0, 1) adjacency matrices. The proposed [JJ] matrix provides distinct set of characteristic polynomial coefficients of the kinematic chains having co-spectral graphs. Therefore, it is verified that the structural invariants ‘SCPC’ and ‘MCPC’ are capable of characterizing all kinematic chains and mechanisms uniquely. Hence, it is possible to detect isomorphism among all the given kinematic chains.

Abstract— With fast evolving technology, it is necessary to design an efficient security system which can detect unauthorized access on any system. The need of the time is to implement an extremely secure, economic and perfect system for face recognition that can protect our system from unauthorized access. So, in this paper, a robust face recognition system approach is proposed for image decomposition using Haar Wavelet Transform, feature extraction of **eigen** **values** using Principal component Analysis (PCA) and then classification using Back Propagation Neural Network (BPNN). Also comparison with the traditional face recognition algorithms is done to show the effectiveness of the proposed algorithm.

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Abstract. Let G be a simple graph with n vertices and m edges. The ordinary energy of the graph is defined as the sum of the absolute **values** of the **Eigen** **values** of its adjacency matrix .This graph invariant is very closely connected to a chemical quantity known as the total π- electron energy of conjugated hydro carbon molecules .In recent times analogous energies are being considered, based on **eigen** **values** of a variety of other graph matrices. We briefly survey this energy of simple graphs. Here we present some basic definitions and techniques used to study energy.

We have studied the variation of Knight Shift with temperature using pseudopotential technique for Zn and Al metals. Knight Shift occurs due to the hyperfine contact interaction between the nucleus and surrounding conduction electrons. The computed **values** of zinc is obtained using H-**eigen** **values** with α = αvt and β = 1 gives K= 0.374 against Kexp = 0.337 at 419 0 C and 0.391 against Kexp = 0.399 at 500 0 C. For Aluminium with H-**eigen** **values** and β = 1 gives K= 0.199 whereas Kexp = 0.164 at 360 0 C and K= 0.209 at 400 0 C for Kexp = 0.184 have been found. The computed **values** and experimental **values** are in good agreement for both metals. It reveals that the Knight Shift increases with increasing temperatures for Zn and Al.

Abstract: In this paper we propose a new BMP based Steganography image identification using **Eigen** **values** and **Eigen** Vectors Technique. This is new approach and this method is different from normal and Steganography image comparison, the steganography technique is normally based on BMP images by hiding information in other information. Many different carrier file formats can be used, but digital images are the most popular because of their frequency on the Internet. For hiding secret information in images, there exists a large variety of steganographic techniques some are more complex than others and all of them have respective strong and weak points. Different applications have different requirements of the steganography technique used. For example, some applications may require absolute invisibility of the secret information, while others require a larger secret message to be hidden. This paper intends to give an overview of steganography image identification using **Eigen** **values** and **Eigen** Vectors Technique. It also attempts to identify the requirements of a good steganographic algorithm and briefly reflects on which steganographic techniques are more suitable for which applications.

In summary, a somewhat straightforward algorithm extracts the **Eigen** **values**, by solving an n degree polynomial, and then derives the **Eigen** space for each **Eigen** value. Some **Eigen** **values** will produce multiple **Eigen** vectors, i.e. an **Eigen** space with more than one dimension. The identity matrix, for instance, has an **Eigen** value of 1, and an n-dimensional **Eigen** space to go with it. In contrast, an **Eigen** value may have multiplicity > 1, yet there is only one **Eigen** vector. This is illustrated by [1,1|0,1], a function that tilts the x axis counter- clockwise and leaves the y axis alone. The **Eigen** **values** are 1 and 1, and the **Eigen** vector is 0,1, namely the y axis.

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The difference of **Eigen** **values** of the test image and the **Eigen** **values** of the database image was found out. Then, it was multiplied with the Euclidean Distance obtained in the first level of classification given as C2 in equation below. Then sum of results obtained for each image were used. One of the most important features of sign language is that each finger in a gesture conveys a particular message and hence each and every finger has to be individually identified as well. In order to assist this requirement, the woolen hand gloves were modified. This was done by replacing and sewing each finger of the glove with a colored cloth for each digit of the hand. Here, we have utilized a unique .color coding for each finger of our hand in order to assist in identifying the fingers. Therefore, segmentation based on various color spaces would be a viable option. In proposed work, two of the most popular color spaces used other than RGB and their conversion from the RGB color space.

In this paper n x n generalized idempotent matrix M is defined with entries 1, -1 satisfying M 2 = mM (1 ≤ m ≤ n) with examples. It is a quite new concept. We have discussed its properties that the Kronecker product of two generalized idempotent matrices is also a generalized idempotent matrix. Also if a n x n matrices M with entries 1 and -1 satisfies M 2 = m M ( 1 ≤ m ≤ n ) then the column of matrix M are **eigen** vector corresponding to **eigen** **values** of M.

3.2 **Eigen** value based detection **Eigen** **values** are scalar **values** called lambda (λ) of a square matrix A, if there is a nontrivial solution of a vector x called **eigen** vector such that: (A -λI) x=0 Or (A- λI) =0. The idea of **Eigen** **values** is used in signal. Detection is to find the noise in signal samples by finding the correlation between samples. Ideally noise samples are uncorrelated with each other. When there is no signal, the received signal covariance matrix become identity matrix multiply by noise power (2I) which results all **Eigen** **values** of the matrix become same as noise power.The main advantage of **Eigen** value based technique is that it does not require any prior information of the PU’s signal and it outperforms Energy detection techniques, especially in the presence of noise covariance uncertainty. 3.3 **Eigen** value Detection Algorithms:

Let D be a digraph with skew-adjacency matrix S(D). The skew energy of D is defined as the sum of the norms of all **eigen** **values** of S(D). Two digraphs are said to be skew equienergetic if their energies are equal. In this paper we obtain the skew laplacian energy S L ~ ( D ) of complete directed bipartite graph K n , 2 and K n , m Mathematics Subject Classification: 05C50, 05C30.

The main advantage of PCA is utilizing it in **Eigen** face approach which helps in decreasing the size of the database for recognition of a test images. This strategy is applied on **Eigen** face way to deal with decrease the element of a huge data set. The basis of the **Eigen** faces method is the PCA. In 1991, Turk and Pentland [15] developed the **Eigen** faces method for recognition of faces by taking 70 images in the training set with success rate of 92% to 100%.In 2004, V. Perlibakas [20] suggested a technique for recognizing face by using Principal Component Analysis and Wavelet decomposition. By applying Wavelet transform with 100 images in the training set a success rate of 80% to 91% has been attained. In 2007 A. Ozdemir [16] suggested object recognition by using **Eigen** vectors. The approach which is discussed is a variant on current approaches to **Eigen** image analysis. Compared to traditional approach this approach gives best recognition rate. In this recognition process the **Eigen** **values** and **Eigen** vectors of the image set is calculated. The image set is nothing but the different positions of the object. In our approach also the above process has been followed. When compared to other methods it is a simple implementation and double-quick recognition. In 2008, F. Kraduman [9] explained face finding method by using Support Vector Machines. In his contribution he achieved 85% to 92.1% as a success rate. Later Neural systems [1] have been proposed by Anjana Mall et al. In this article the frame work works in two phases. The main part is a neural system that gets as information a 20X20 pixel region of the image, and generates an output ranging from 1 to -1. It decides whether face is presented or not. In 2008, K. Kim et al. [10] showed