We present a practical and efficient means to compute the singular value decomposition (svd) of a quaternion matrix A based on bidiagonalization of A to a real bidiagonal matrix B using quaternionic Householder transformations. Computation of the svd of B using an existing subroutine library such as lapack provides the singular values of A. The singular vectors of A are obtained trivially from ...

I Transformations and Projections 5 2 Camera Models 5 3 Plane to plane transformations 9 3.1 Plane projectivities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3.2 Homogeneous line representation . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.3 Duality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.4 Projective tra...

We apply generalized Bogoliubov transformations to the transfer matrix of relativistic field theories regularized on a lattice. We derive the conditions these transformations must satisfy to factorize the transfer matrix into two terms which propagate fermions and antifermions separately, and we solve the relative equations under some conditions. We relate these equations to the saddle point ap...

This paper describes two methods for computing the invariant subspace of a matrix. The rst method involves using transformations to interchange the eigenvalues. The matrix is assumed to be in Schur form and transformations are applied to interchange neighboring blocks. The blocks can be either one by one or two by two. The second method involves the construction of an invariant subspace by a di...

The aim of the present work is to introduce the concept of $lambda _{r}$-almost convergence of sequences. We define the spaces $fleft( lambda _{r}right) $ and $f_{0}left( lambda _{r}right) $ of $ lambda _{r}$-almost convergent and $lambda _{r}$-almost null sequences. We investigate some inclusion relations concerning those spaces with examples and we determine the $beta $- and $gamma $-duals of...

A new framework for transforming arbitrary matrices to compressed representations is presented. The framework provides a generic way of transforming a matrix via unitary similarity transformations to e.g. Hessenberg, Hessenberg-like and combinations of both. The new algorithms are deduced, based on the QR-factorization of the original matrix. Based on manipulations with Givens transformations, ...

The beam transfer matrix, often called the ABCD matrix, is one of the essential mathematical instruments in optics. It is a unimodular matrix whose determinant is 1. If all the elements are real with three independent parameters, this matrix is a 2 x 2 representation of the group Sp(2). It is shown that a real ABCD matrix can be generated by two shear transformations. It is then noted that, in ...

We introduced matrices as a computational tool for working with linear transformations between finitely generated vector spaces. The general properties of linear transformations and the algebraic operations on them — addition, multiplication by scalars and composition — enabled us to define corresponding algebraic operations on matrices — matrix addition, multiplication by scalars and matrix mu...

In [P90] we proposed to employ Vandermonde and Hankel multipliers to transform into each other the matrix structures of Toeplitz, Hankel, Vandermonde and Cauchy types as a means of extending any successful algorithm for the inversion of matrices having one of these structures to inverting the matrices with the structures of the three other types. Surprising power of this approach has been demon...

According to V.P.Potapov, a classical interpolation problem can be reformulated in terms of a so-called Fundamental Matrix Inequality (FMI). To show that every solution of the FMI satisfies the interpolation problem, we usualy have to transform the FMI in some special way. In this paper the number of of transformations of the FMI which come into play are motivated and demonstrated by simple, bu...