Quaternion Matrix Computations

Musheng Wei, Ying Li, Fengxia Zhang and Jianli Zhao
Liaocheng University, Shandong, P. R. China

Series: Mathematics Research Developments
BISAC: MAT029000

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Edited by I Leslie Rubin, Robert J Geller, Abby Mutic, Benjamin A Gitterman, Nathan Mutic, Wayne Garfinkel, Claire D Coles, Kurt Martinuzzi, and Joav Merrick

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In this monograph, the authors describe state-of-the-art real structure-preserving algorithms for quaternion matrix computations, especially the LU, the Cholesky, the QR and the singular value decomposition of quaternion matrices, direct and iterative methods for solving quaternion linear systems, generalized least squares problems, and quaternion right eigenvalue problems. Formulas of the methods are derived, and numerical codes are provided which utilize advantages of real structure-preserving of quaternion matrices and high-level performance of vector pipelining arithmetic operations, using Matlab software. These algorithms are very efficient and stable. This monograph can be used as a reference book for scientists, engineers and researchers in color image processing, quaternionic quantum mechanics, information engineering, information security and scientific computing. It can also act as a textbook at the graduate level in related areas.

 

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Preface

Notation

Chapter 1. Preliminaries

Chapter 2. Computing Matrix Decompositions

Chapter 3. Linear System and GLS

Chapter 4. Direct Methods for Linear System and GLS

Chapter 5. Iterative Methods for Linear System and GLS

Chapter 6. Quarternion Eigenvalue Problems

About the Authors

Bibliography

Keywords: Quaternion matrices, real structure-preserving, quantum mechanics, color image, color watermark.

Audience: Scientists, engineers and researchers in color image processing, quaternionic quantum mechanics, information engineering, information security and scientific computing, or graduate student level in related areas.

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