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...

In this paper, the concept of ultrametric structure is intertwined with SLAM procedure. A set pre-existing transformations has been used to create a new simultaneous localization and mapping (SLAM) algorithm. We have developed two parallel algorithms that implement time-consuming Boolean space dissimilarity matrix. The resulting matrix an important input vector quantization (VQ) step in process...

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...

In 1977, Jacob defines Gα, for any 0 ≤ α <∞, as the set of all complex sequences x such that limsup|xk|1/k ≤ α. In this paper, we apply Gu −Gv matrix transformation on the sequences of operators given in the famous Walsh’s equiconvergence theorem, where we have that the difference of two sequences of operators converges to zero in a disk. We show that the Gu −Gv matrix transformation of the dif...

We first recall some properties of infinite tridiagonal matrices considered as matrix transformations in sequence spaces of the forms sξ , sξ , s (c) ξ , or lp(ξ). Then, we give some results on the finite section method for approximating a solution of an infinite linear system. Finally, using a quasi-Newton method, we construct a sequence that converges fast to a solution of an infinite linear ...