Hermite and Smith normal form are important forms of matrices used in linear algebra. These terms have many applications in group theory and number theory. As the entries of the matrix and of its corresponding transformation matrices can explode during the computation, it is a very difficult problem to compute the Hermite and Smith normal form of large dense matrices. The main problems of the c...

This paper studies the possibility of achieving indistinguishabilitybased security in privately outsourcing linear equation systems over real numbers. The particular task is to solve a full-rank n× n system Ax = b. Since the most complex part of this task is inverting A, the problem can be reduced to outsourcing of a square matrix inverse computation. Although outsourcing matrix inverse is triv...

Dirac matrices, also known as gamma matrices, are defined only up to a similarity transformation. Usually, some explicit representation of these matrices is assumed in order to deal with them. In this article, we show how it is possible to proceed without any explicit form of these matrices. Various important identities involving Dirac matrices and spinors have been derived without assuming any...

In the paper it is investigated, under which conditions a time variable state transformation can be used to change a periodic autonomous system realization into a form with constant real coefficients. Conditions for the transformation to be periodic are further considered, and it is shown that the necessary and sufficient condition to meet the conditions is in that two specific matrices must be...

This paper is concerned with accurate computations for matrix multiplication. An error-free transformation of matrix multiplication is developed by the authors. It transforms a product of two floatingpoint matrices to a sum of several floating-point matrices by using only floating-point arithmetic. This transformation is useful not only for accurate matrix multiplication but also for interval e...

The notion of a common canonical form for a sequence of square matrices is introduced. Necessary and sufficient conditions for the existence of a similarity transformation reducing the sequence of matrices to the common canonical form are established. It is shown that (i) using a suitable state vector linear transformation it is possible to decompose a linear 2D system into two linear 2D subsys...

By using an extension of Desargues theorem, and the extended Desarguesian configuration thereof, the analytical definition for the stereohomology geometric transformation in projective geometry is proposed in this work. A series of such commonly used geometric transformations in computer graphics as central projection, parallel projection, centrosymmetry, reflection and translation transformati...

Calibration of a structured light system is considered in this paper. The system consists of a projector whose output is controlled by a liquid crystal shutter, and a camera to capture the images. A sequence of patterns is projected to temporally encode 256 stripes on the visible surfaces. The transformation from 3D world coordinates to camera image plane coordinates and projector stripe ids ar...

When it becomes necessary to reduce the complexity of a classifier, dimensionality reduction can be an effective way to address classifier complexity. Linear Discriminant Analysis (LDA) is one approach to dimensionality reduction that makes use of a linear transformation matrix. The widely used Fisher’s LDA is “sub-optimal” when the sample class covariance matrices are unequal, meaning that ano...

Steganography is meant for covert communication of confidential data through internet. In this paper, we propose Steganography based on Payload Transformation (SPT) which is non LSB and non transform domain technique where the cover image is segmented into 2*2 matrices and the matrix for payload embedding is considered based on the threshold value fixed by computing adjacent pixel intensity dif...