Unimodular Matrix with Layered Compound Structure and Its Transformation Theory

Hua Ma

doi:doi:10.11648/j.ml.20200601.11

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Unimodular Matrix with Layered Compound Structure and Its Transformation Theory

Hua Ma

Published in Mathematics Letters (Volume 6, Issue 1)

Received: 7 May 2020 Accepted: 22 May 2020 Published: 28 May 2020

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Abstract

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.

Published in	Mathematics Letters (Volume 6, Issue 1)
DOI	10.11648/j.ml.20200601.11
Page(s)	1-5
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2020. Published by Science Publishing Group

Keywords

Unimodular Compound Matrix, Special Unitary Group, Symmetric Transformation, Intrinsic Space, Pauli Matrix, Dirac Algebra, Euler Equation

References

[1]	David S. Watkins, Fundamentals of Matrix Computations (Wiley, 2013).
[2]	Riley, Kenneth F., Hobson, Michael P., Bence, Stephen J., Mathematical methods for physics and engineering (Cambridge University Press, 1997).
[3]	J. J. Sakurai, Modern Quantum Mechanics (Massachusetts: Addison-Wesley, 1995).
[4]	D. McMahon, Quantum Mechanics Demystified (Mc Graw Hill (USA), 2006).
[5]	F. Mandl, G. Shaw, Quantum Field Theory (John Wiley & Sons, 1993).
[6]	Wherrett, Brian S., Group Theory for Atoms, Molecules and Solids (Prentice–Hall International, 1987).
[7]	Benjamin Passer, Shape, scale, and minimality of matrix ranges. Trans. Amer. Math. Soc. 372 (2019) 1451-1484.
[8]	Braxton O. and Dong W., A diffusion generated method for orthogonal matrix-valued fields. Math. Comp. 89 (2020) 515-550.
[9]	Adel A., Hamed A., S. K. Jain and Efim Z.. Matrix wreath products of algebras and embedding theorems. Trans. Amer. Math. Soc. 372 (2019) 2389-2406.
[10]	Mikael L., Santeri M. and Niklas W. Norm estimates of weighted composition operators pertaining to the Hilbert matrix. Proc. Amer. Math. Soc. 147 (2019) 2425-2435.
[11]	Brown, William A., Matrices and vector spaces (New York, NY: M. Dekker, 1991, ISBN 978-0-8247-8419-5).
[12]	Philip N. Klein, Coding the Matrix: Linear Algebra through Applications to Computer Science (Newtonian Press, 2013).
[13]	Rajendra Bhatia, Positive definite matrices (Princeton Series in Applied Mathematics, 2007).

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Hua Ma. (2020). Unimodular Matrix with Layered Compound Structure and Its Transformation Theory. Mathematics Letters, 6(1), 1-5. https://doi.org/10.11648/j.ml.20200601.11

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ACS Style

Hua Ma. Unimodular Matrix with Layered Compound Structure and Its Transformation Theory. Math. Lett. 2020, 6(1), 1-5. doi: 10.11648/j.ml.20200601.11

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AMA Style

Hua Ma. Unimodular Matrix with Layered Compound Structure and Its Transformation Theory. Math Lett. 2020;6(1):1-5. doi: 10.11648/j.ml.20200601.11

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@article{10.11648/j.ml.20200601.11,
  author = {Hua Ma},
  title = {Unimodular Matrix with Layered Compound Structure and Its Transformation Theory},
  journal = {Mathematics Letters},
  volume = {6},
  number = {1},
  pages = {1-5},
  doi = {10.11648/j.ml.20200601.11},
  url = {https://doi.org/10.11648/j.ml.20200601.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ml.20200601.11},
  abstract = {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.},
 year = {2020}
}

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TY  - JOUR
T1  - Unimodular Matrix with Layered Compound Structure and Its Transformation Theory
AU  - Hua Ma
Y1  - 2020/05/28
PY  - 2020
N1  - https://doi.org/10.11648/j.ml.20200601.11
DO  - 10.11648/j.ml.20200601.11
T2  - Mathematics Letters
JF  - Mathematics Letters
JO  - Mathematics Letters
SP  - 1
EP  - 5
PB  - Science Publishing Group
SN  - 2575-5056
UR  - https://doi.org/10.11648/j.ml.20200601.11
AB  - 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.
VL  - 6
IS  - 1
ER  -

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Author Information

Hua Ma

College of Science, Air Force University of Engineering, Xi’an, People’s Republic of China

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APA Style

Hua Ma. (2020). Unimodular Matrix with Layered Compound Structure and Its Transformation Theory. Mathematics Letters, 6(1), 1-5. https://doi.org/10.11648/j.ml.20200601.11

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ACS Style

Hua Ma. Unimodular Matrix with Layered Compound Structure and Its Transformation Theory. Math. Lett. 2020, 6(1), 1-5. doi: 10.11648/j.ml.20200601.11

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AMA Style

Hua Ma. Unimodular Matrix with Layered Compound Structure and Its Transformation Theory. Math Lett. 2020;6(1):1-5. doi: 10.11648/j.ml.20200601.11

Copy | Download

@article{10.11648/j.ml.20200601.11,
  author = {Hua Ma},
  title = {Unimodular Matrix with Layered Compound Structure and Its Transformation Theory},
  journal = {Mathematics Letters},
  volume = {6},
  number = {1},
  pages = {1-5},
  doi = {10.11648/j.ml.20200601.11},
  url = {https://doi.org/10.11648/j.ml.20200601.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ml.20200601.11},
  abstract = {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.},
 year = {2020}
}

Copy | Download

TY  - JOUR
T1  - Unimodular Matrix with Layered Compound Structure and Its Transformation Theory
AU  - Hua Ma
Y1  - 2020/05/28
PY  - 2020
N1  - https://doi.org/10.11648/j.ml.20200601.11
DO  - 10.11648/j.ml.20200601.11
T2  - Mathematics Letters
JF  - Mathematics Letters
JO  - Mathematics Letters
SP  - 1
EP  - 5
PB  - Science Publishing Group
SN  - 2575-5056
UR  - https://doi.org/10.11648/j.ml.20200601.11
AB  - 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.
VL  - 6
IS  - 1
ER  -

Copy | Download