107,975 research outputs found
A Symbolic Algorithm for Computation of Non-degenerate Clifford Algebra Matrix Representations
Clifford algebras are an active area of mathematical research. The main
objective of the paper is to exhibit a construction of a matrix algebra
isomorphic to a Clifford algebra of signature (p,q), which can be automatically
implemented using general purpose linear algebra software. While this is not
the most economical way of implementation for lower-dimensional algebras it
offers a transparent mechanism of translation between a Clifford algebra and
its isomorphic faithful real matrix representation. Examples of lower
dimensional Clifford algebras are presented.Comment: 220 page
On the Efficacy and High-Performance Implementation of Quaternion Matrix Multiplication
Quaternion symmetry is ubiquitous in the physical sciences. As such, much
work has been afforded over the years to the development of efficient schemes
to exploit this symmetry using real and complex linear algebra. Recent years
have also seen many advances in the formal theoretical development of
explicitly quaternion linear algebra with promising applications in image
processing and machine learning. Despite these advances, there do not currently
exist optimized software implementations of quaternion linear algebra. The
leverage of optimized linear algebra software is crucial in the achievement of
high levels of performance on modern computing architectures, and thus provides
a central tool in the development of high-performance scientific software. In
this work, a case will be made for the efficacy of high-performance quaternion
linear algebra software for appropriate problems. In this pursuit, an optimized
software implementation of quaternion matrix multiplication will be presented
and will be shown to outperform a vendor tuned implementation for the analogous
complex matrix operation. The results of this work pave the path for further
development of high-performance quaternion linear algebra software which will
improve the performance of the next generation of applicable scientific
applications
Design Graphical User Interface of Linear Algebra System Package by Using MATLAB
The Linear Algebra package offers routines to construct and manipulate Matrices and Vectors, compute standard operations, query results and solve linear algebra problems. This Linear Algebra package implements a vast array of common linear algebra functions. This library is intended to be completely self-contained and instructive to the interested user. In this paper a developed Software Package based on Graphical User Interface (GUI) using MATLAB is proposed which can be used for students and researchers in Mathematics. This package consists of two main modules; the first one deal with applying main important methods of linear algebra system (Gauss elimination, practical solution, least square solution and a square solution, Invertible).While in the second introduces some important explanation of linear algebra system as well as has created significant examination testing for students that related to linear algebra. In summary, this Software Package is designed and implemented in simple way and user friendly as well as it is very easy to use and apply any methods , so it can be easily used by students/ researchers using only standalone application or executable file (exe file) without installing MATLAB program
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