In this paper, we show that the eigenvectors of the zero Laplacian and signless Lapacian eigenvalues of a k-uniform hypergraph are closely related to some configured components of that hypergraph. We show that the components of an eigenvector of the zero Laplacian or signless Lapacian eigenvalue have the same modulus. Moreover, under a canonical regularization, the phases of the components of t...

Ensemble and reduced-rank approaches to prediction and assimilation rely on low-dimensional approximations of the estimation error covariances. Here stability properties of the forecast/ analysis cycle for linear, time-independent systems are used to identify factors that cause the steady-state analysis error covariance to admit a low-dimensional representation. A useful measure of forecast/ana...

A real symmetric matrix of order n has a full set of orthogonal eigenvectors. The most used approach to compute the spectrum of such matrices reduces first the dense symmetric matrix into a symmetric structured one, i.e., either a tridiagonal matrix [2, 3] or a semiseparable matrix [4]. This step is accomplished in O(n) operations. Once the latter symmetric structured matrix is available, its s...

Applications related to artificial intelligence, machine learning, and system identification simulations essentially use eigenvectors. Calculating eigenvectors for very large matrices using conventional methods is compute-intensive renders the applications slow. Recently, Eigenvector-Eigenvalue Identity formula promising significant speedup was identified. We study algorithmic implementation of...

A novel Eigenstructure Assignment (ESA) method for vibration confinement of flexible structures has been developed. This method is an output feedback control and determines the closed-loop systems that their eigenvectors are orthogonalized to the open-loop eigenvectors. This method is a numerical method and used Singular Value Decomposition (SVD) to find the null space of the closed-loop eigenv...

This paper presents a technique for animating a threedimensional face model through the application of Principal Component Analysis (PCA). Using PCA has several advantages over traditional approaches to facial animation because it reduces the number of parameters needed to describe a face and confines the facial motion to a valid space to prevent unnatural contortions. First real data is optica...

The numerical computation of derivatives of eigenvalues and eigenvectors has been an active research topic due to its wide applications in engineering and the physical sciences. There are many numerical methods available in the literatures for computing derivatives of eigenvalues and eigenvectors for standard eigenvalue problems and quadratic eigenvalue problems. However, almost all existing me...

1≤i,j≤n denote the n×n matrix formed by right justifying the first n rows of Pascal’s triangle. Let a denote the golden ratio (1+ √ 5)/2. We will show that the eigenvalues of R are λj = (−1)n+ja2j−n−1, 1 ≤ j ≤ n, (as conjectured in [1]), with corresponding eigenvectors uj = (uij)1≤i≤n where uij = ∑j k=1(−1) ( i−1 k−1 )(n−i j−k ) a2k−i−1. Since the eigenvalues are distinct, the eigenvectors are ...

Given an eigenvalue of a symplectic matrix, we analyze its change under small structure-preserving perturbations, i.e., perturbations which maintain the symplectic nature of the matrix. Modelling such perturbations multiplicatively allows us to make use of the first order multiplicative perturbation theory developed in [2] via Newton diagram techniques. This leads to both leading exponents and ...

In this paper, we show that the eigenvectors associated with the zero eigenvalues of the Laplacian and signless Lapacian tensors of a k-uniform hypergraph are closely related to some configured components of that hypergraph. We show that the components of an eigenvector associated with the zero eigenvalue of the Laplacian or signless Lapacian tensor have the same modulus. Moreover, under a cano...