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On Complex representations of the Clifford algebras
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In this paper, we establish a complex matrix representation of the Clifford algebra $C\ell_{p,q}$. The size of our representation is significantly smaller than the size of the elements in $L_{p,q}(\mathbb{R})$. Additionally, we give detailed information about the spectrum of the constructed matrix representation.
Abstract
In this paper, we establish a complex matrix representation of the Clifford algebra $C\ell_{p,q}$. The size of our representation is significantly smaller than the size of the elements in $L_{p,q}(\mathbb{R})$. Additionally, we give detailed information about the spectrum of the constructed matrix representation.
참고문헌 (10)
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- R. A. Horn, "Matrix Analysis" (1985), Cambridge University Press
- D. Lee, "Extension of algebras and its applications to the real Clifford algebras", Linear Multilinear Algebra, 64(11), pp.2241~2251 (2016)[DOI]
- C. P. Poole, Jr., "Pauli-Dirac matrix generators of Clifford algebras", Found. Phys, 12(7), pp.719~738 (1982)[DOI]
- Y. Song, "A construction of matrix representation of Clifford algebras", Adv. Appl. Clifford Algebr, 25(3), pp.719~731 (2015)[DOI]
- Y. Song, "Vector generators of the real Clifford algebras", Linear Multilinear Algebra, 63(12), pp.2448~2460 (2015)[DOI]
- Y. Tian, "Universal similarity factorization equalities over real Clifford algebras", Adv. Appl. Clifford Algebras, 8(2), pp.365~402 (1998)[DOI]
- F. Zhang, "Gerˇsgorin type theorems for quaternionic matrices", Linear Algebra Appl, 424(1), pp.139~153 (2007)[DOI]
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