Unimodular Matrix with Layered Compound Structure and Its Transformation Theory
Mathematics Letters
Volume 6, Issue 1, March 2020, Pages: 1-5
Received: May 7, 2020; Accepted: May 22, 2020; Published: May 28, 2020
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Hua Ma, College of Science, Air Force University of Engineering, Xi’an, People’s Republic of China
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Unimodular compound structural matrix and the transformation theory are studied. Conceptually, unimodular compound structural matrix is a matrix set with layered compound structure constructed by taking some special original matrix as element and structure mode, thus having some basic properties such as unimodular, orthogonality and symmetry. Theoretically, the transformation theory of unimodular matrix have been established, using which the natural exponential matrix function of real variable and unimodular matrix can be solved efficiently; and when it is applied to the transformation of vector variable, the transformation law of variables and the invariants related to the matrix symmetry have obtained general conclusions. The results of this study are the extension of Pauli matrix, Dirac algebra and Euler equation, thus have potential applications in mathematics and physics: mathematically, which can be used as compound special matrixes to describe the compound special unitary group, to construct the algebraic structure of layered linear space, and to analytically calculate the exponential function of unimodular matrix; physically, which can be used to describe the new symmetry of intrinsic space, to express the recombination of basic particle structures, and to analysis the correlation transformation of physical mechanism.
Unimodular Compound Matrix, Special Unitary Group, Symmetric Transformation, Intrinsic Space, Pauli Matrix, Dirac Algebra, Euler Equation
To cite this article
Hua Ma, Unimodular Matrix with Layered Compound Structure and Its Transformation Theory, Mathematics Letters. Vol. 6, No. 1, 2020, pp. 1-5. doi: 10.11648/j.ml.20200601.11
Copyright © 2020 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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