We utilize group-theoretical methods to develop a matrix representation of differential operators that act on tensors of any rank. In particular, we concentrate on the matrix formulation of the curl operator. A self-adjoint matrix of the curl operator is constructed and its action is extended to a complex plane. This scheme allows us to obtain properties, similar to those of the traditional cur...

Let X and Y be two sequence spaces and A = (ank) be an infinite matrix. If for each x ∈ X the series An(x) = ∑∞ k=0 ankxk converges for each n and the sequence Ax = (Anx) ∈ Y we say that the matrix A maps X into Y . By (X,Y ) we denote the set of all matrices which map X into Y . Let c be the set of all convergent sequences. A matrix A is called regular if A ∈ (c, c) and limn→∞Anx = limk→∞ xk f...

Subspace clustering refers to the problem of segmenting a set of data points approximately drawn from a union of multiple linear subspaces. Aiming at the subspace clustering problem, various subspace clustering algorithms have been proposed and low rank representation based subspace clustering is a very promising and efficient subspace clustering algorithm. Low rank representation method seeks ...

A matrix representation of iterative methods is presented which includes almost all those based on polynomial methods. A simple lemma and corollaries are established which show that the order of convergence of the iteration is the spectral radius of the matrix representation. A number of old and new methods, particularly those adapted to parallel computation, are analyzed using this representat...

Existing work on the representation of operators in one-dimensional, compactly-supported, orthonormal wavelet bases is extended to two dimensions. The non-standard form of the representation of operators is given in separable two-dimensional, periodic, orthonormal wavelet bases. The matrix representation of the partial differential operators ∂x and ∂y are constructed and a closed form formula f...

Randomized sampling has recently been proven a highly efficient technique for computing approximate factorizations of matrices that have low numerical rank. This paper describes an extension of such techniques to a wider class of matrices that are not themselves rank-deficient, but have off-diagonal blocks that are; specifically, the class of so called Hierarchically Semi-Separable (HSS) matric...

Being symmetric positive-definite (SPD), covariance matrix has traditionally been used to represent a set of local descriptors in visual recognition. Recent study shows that kernel matrix can give considerably better representation by modelling the nonlinearity in the local descriptor set. Nevertheless, neither the descriptors nor the kernel matrix is deeply learned. Worse, they are considered ...

In this paper we introduce a Givens-weight representation for rank structured matrices, where the rank structure is defined by certain low rank submatrices starting from the bottom left matrix corner. This representation will be compared to the (block) quasiseparable representations occurring in the literature. We will then provide some basic algorithms for the Givens-weight representation, in ...

Three-Dimensional Rotations as Products of Simpler Rotations 1. The most general 3 × 3 rotation matrix In a class handout entitled, Three-Dimensional Proper and Improper Rotation Matrices, I derived the following general form for a 3× 3 matrix representation of a proper rotation by an angle θ in a counterclockwise direction about a fixed rotation axis parallel to the unit vector n̂ = (n1, n2, n3...

as a significant number of post-colonial writers have reread colonial masterpieces, the main purpose of the researchers in this study is a detailed analysis of among the believers by v. s. naipaul in the light of orientalism.this article is indeed a response to the representation of the orient, islam, and the islamic middle east in the west, in general, and in naipaul’s travel writing, in parti...