Eigenvectors

The transmission of vibrations between coupled subsystems is treated by using coupling eigenvalues and eigenvectors. It is demonstrated through a basic equation that coupling eigenvalues and eigenvectors characterize the energy exchanges between subsystems due to the coupling. The coupling eigenvalue relates to the coupling strength and coupling eigenvectors to the coupling transmission path. In addition, in the case of several couplings, a simplified method is presented in which only the prevailing modal path between subsystems is used. The results obtained by using this method compare well with the reference calculation. The transmission of vibrations by coupling can be calculated with a small number of variables and offers a new perspective in the range of medium frequency.

The map which takes a square matrix to its tropical eigenvalue-eigenvector pair is piecewise linear. We determine the cones of linearity of this map. They are simplicial but they do not form a fan. Motivated by statistical ranking, we also study the restriction of that cone decomposition to the subspace of skew-symmetric matrices.

T I. INTRODUCTION HIS paper deals with some mathematical aspects of the discrete Fourier transform (DFT), studied with linear algebra and matrix theory methods. The vast majority of papers on the DFT have concerned computational issues, most notably the extensive literature ...

Using the Stochastic Finite Element Method (SFEM) to perform reliability analysis of the free vibration of composite plates with material and fabrication uncertainties has received much attention lately. In this work the stochastic analysis is performed using the First-Order Reliability Method (FORM-method 2) and the Second-Order Reliability Method (SORM). The basic random variables include laminae stiffness properties and material density, as well as the randomness in ply orientation angles. Modeling of the composite behavior utilizes a nine-noded isoparametric Lagrangian element based on the third-order shear deformation theory. Calculating the eigenvectors at the mean values of the variables proves to be a reasonable simplification which significantly increases solution speed. The stochastic finite element code is validated using comparisons with results of Monte Carlo simulation technique with importance sampling. Results show that SORM is an excellent rapid tool in the stochastic analysis of free vibration of composite plates, when compared to the slower Monte Carlo simulation techniques.

Face recognition has been largely used in biometric field as a security measure at air ports, passport verif ication, criminals ' list verification, visa processing, and so on. Various literature studies suggested different approaches for face recognition systems and most of these studies have limitations with low performance rates. Eigenfaces and principle component analysis (PCA) can be considered as most important face recognition approaches in the literature. There is a need to develop algorithms and approaches that overcome these disadvantages and improve performance of face recognition systems. At the same time, there is a lack of literature studies which are related to face recognition systems based on EigenFaces and PCA. Therefore, this work includes a comparative study of literature researches related to Eigenfaces and PCA for face recognition systems. The main steps, strengths and limitations of each study will be discussed. Many recommendations were suggested in this...

Feature recognition is one of the most prominent areas of Machine Learning (ML) since ages together human are fascinated with the world of colors, features, virtues, and such artifacts for gaining inside into the knowledge sharing. The intuitiveness of the human mind is quite capable of recognizing and pursing miniature details about the surroundings and the environment where they live in. In so far, even the animals and other living beings also have the power to recognize and assimilate the information─ however, they lack in understanding, interpolation and other feature extraction details.
The traditional AI has been used for various applications starting from feature detection, extraction and applying convolution techniques for feature engineering. In achieving so Principal Component Analysis (PCA) gives a mathematical model to get inside with reduction feature extraction and computational ef iciency. This image processing area has being fascination for humans to see nice features and increase their happiness quotient.
On the other side, the people are playing the game to reshape the feature and get a noticed like criminals, terrorists, fraudulent and other such irrelevant human behavior. However some of the features never changes through the life span of like retina, lines or regions on the hand, thumb impression etc., This salient features are going to be retain throughout the life journey and everlasting.
In this article an attempt is being made to use ML algorithms for such areas and with pertinent mathematical background; thereby we can understand certain artifacts of features and use them for a good cause.

Face recognition has been largely used in biometric field as a security measure at air ports, passport verification, criminals' list verification, visa processing, and so on. Various literature studies suggested different approaches for face recognition systems and most of these studies have limitations with low performance rates. Eigenfaces and principle component analysis (PCA) can be considered as most important face recognition approaches in the literature. There is a need to develop algorithms and approaches that overcome these disadvantages and improve performance of face recognition systems. At the same time, there is a lack of literature studies which are related to face recognition systems based on EigenFaces and PCA. Therefore, this work includes a comparative study of literature researches related to Eigenfaces and PCA for face recognition systems. The main steps, strengths and limitations of each study will be discussed. Many recommendations were suggested in this st...

Recently, we have shown how the interpretation of quantum mechanics due to Lande' can be used to derive from first principles generalized formulas for the operators and some eigenvectors for spin 1/2 Though we gave the operators for all the components of the spin, we did not give the eigenvectors of the operators for the x and y components of the spin. We now give these vectors. In addition, we present a new and simple method of deriving the operators for the x and y components of the spin as well as their vectors from those for the z component. We give a general proof that the operator for the square of the spin is the unit matrix multiplied by the value of the square of the spin.