Two Different Computing Methods of the Smith Arithmetic Determinant
The Smith arithmetic determinant is investigated in this paper. By using two different methods, we derive the explicit formula for the Smith arithmetic determinant.
[1] Tingzhu Huang, Junhua He and Yongbin Li, Advanced Algebra, Higer Education Press, Beijing, 2011.
[2] Chengdong Pan and Chengbiao Pan, Elementary Number Theory, Beijing University Press, Beijing, 1998.
[3] Brualdi and Richard A, Combinatorial Matrix Theory, Cambridge University Press, Cambridge, 1992.
[4] Beslin S and Ligh S, Greatest common divisor matrices(J), Linear Algebra Appl, 1989, 118:69-76.
[5] McCarthy P J, A generalized of Smith’s determinant(J), Canadian Math. Bull, 1986, 29:109-113.
[6] Beslin S and el Kassar N, GCD matrices and Smith’s determinant for a U.F.D.(J), Bull. Number Theory, 1989, 8:23-28.
[1] Tingzhu Huang, Junhua He and Yongbin Li, Advanced Algebra, Higer Education Press, Beijing, 2011.
[2] Chengdong Pan and Chengbiao Pan, Elementary Number Theory, Beijing University Press, Beijing, 1998.
[3] Brualdi and Richard A, Combinatorial Matrix Theory, Cambridge University Press, Cambridge, 1992.
[4] Beslin S and Ligh S, Greatest common divisor matrices(J), Linear Algebra Appl, 1989, 118:69-76.
[5] McCarthy P J, A generalized of Smith’s determinant(J), Canadian Math. Bull, 1986, 29:109-113.
[6] Beslin S and el Kassar N, GCD matrices and Smith’s determinant for a U.F.D.(J), Bull. Number Theory, 1989, 8:23-28.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:65817", author = "Xing-Jian Li and Shen Qu", title = "Two Different Computing Methods of the Smith Arithmetic Determinant", abstract = "The Smith arithmetic determinant is investigated in this paper. By using two different methods, we derive the explicit formula for the Smith arithmetic determinant.
", keywords = "Elementary row transformation, Euler function, Matrix decomposition, Smith arithmetic determinant.", volume = "7", number = "1", pages = "182-5", }