四元数矩阵的新特征值定位
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摘要
针对四元数矩阵的特征值定位问题,得到一类新的左特征值定位集与右特征值定位集,改进了已有结果,并通过例子说明结果的有效性.
For the eigenvalue localization problem of quaternionic matrices, a new set locating left and right eigenvalues of quaternionic matrices is obtained respectively, which improves some existing results. An example is given to illustrate the effectiveness of the results.
For the eigenvalue localization problem of quaternionic matrices, a new set locating left and right eigenvalues of quaternionic matrices is obtained respectively, which improves some existing results. An example is given to illustrate the effectiveness of the results.
引文
[1] Zhang F. Quaternions and matrices of quaternions[J]. Linear Algebra and Its Applications,1997,251(2):21-57.
[2] Davies A J, Mckellar B H J. Observability of quaternionic quantum mechanics[J]. Physical Review A, 1992,46(7):3671-3675.
[3] Dixon G M. Division Algebras:Octonions, Quaternions, Complex Numbers and the Algebraic Design of Physics[M]. US:Kluwer Academic Publishers, 1994.
[4] Cohen N, De Leo S. The quaternionic determinant[J]. Electron. J. Linear Algebra, 2000,20(1):100-111.
[5] Cohn P M. Skew Field Constructions[M]. England:Cambridge University Press, 1977.
[6] Davies A J, Mckellar B H. Nonrelativistic quaternionic quantum mechanics in one dimension[J].Physical Review A, 1989,40(8):4209-4214.
[7] Finkelstein D, Jauch J M, Speiser D. Quaternionic representations of compact groups[J]. Journal of Mathematical Physics, 1963,4(1):136-140.
[8] Rader C M, Steinhardt A O. Hyperbolic householder transformations[J]. SIAM Journal on Matrix Analysis&Applications, 2006,9(2):1589-1602.
[9] Steinhardt A O. Householder transforms in signal processing[J]. IEEE ASSP Magazine, 1988,5(3):4-12.
[10] Wang Q. Quaternion transformation and its application to the displacement analysis of spatial mechanisms[J]. Acta Mechanica Sinica, 1983,(1):56-63.
[11]许方官,陆元荣.四元数在量子力学中的应用[J].大学物理, 2001,20(11):20-23.
[12] Liu Yusu, Zhang Xiuping. Some properties on quaternionic matrices[J]. Journal of Beijing Normal University, 2015,4(2):5-18.
[13]黄礼平.四元数矩阵的特征值与奇异值估计[J]. Journal of Mathematical Research with Applications, 1992,12(3):449-454.
[14] Zhang F. Gerschgorin type theorems for quaternionic matrices[J]. Linear Algebra&Its Applications, 2007,424(1):139-153.
[14] Wu J L. Distribution and estimation for eigenvalues of real quaternion matrices[J]. Computers&Mathematics with Applications, 2008,55(9):1998-2004.
[16]李文亮.四元数矩阵[M].长沙:国防科技大学出版社, 2002.
[17]邓勇,黄敬频.四元数体上一类矩阵方程解的数值方法[J].纯粹数学与应用数学, 2010,26(5):705-709.
[18] Zou L, Jiang Y, Wu J. Location for the right eigenvalues of quaternion matrices[J]. Journal of Applied Mathematics&Computing, 2012,38(1-2):71-83.
[2] Davies A J, Mckellar B H J. Observability of quaternionic quantum mechanics[J]. Physical Review A, 1992,46(7):3671-3675.
[3] Dixon G M. Division Algebras:Octonions, Quaternions, Complex Numbers and the Algebraic Design of Physics[M]. US:Kluwer Academic Publishers, 1994.
[4] Cohen N, De Leo S. The quaternionic determinant[J]. Electron. J. Linear Algebra, 2000,20(1):100-111.
[5] Cohn P M. Skew Field Constructions[M]. England:Cambridge University Press, 1977.
[6] Davies A J, Mckellar B H. Nonrelativistic quaternionic quantum mechanics in one dimension[J].Physical Review A, 1989,40(8):4209-4214.
[7] Finkelstein D, Jauch J M, Speiser D. Quaternionic representations of compact groups[J]. Journal of Mathematical Physics, 1963,4(1):136-140.
[8] Rader C M, Steinhardt A O. Hyperbolic householder transformations[J]. SIAM Journal on Matrix Analysis&Applications, 2006,9(2):1589-1602.
[9] Steinhardt A O. Householder transforms in signal processing[J]. IEEE ASSP Magazine, 1988,5(3):4-12.
[10] Wang Q. Quaternion transformation and its application to the displacement analysis of spatial mechanisms[J]. Acta Mechanica Sinica, 1983,(1):56-63.
[11]许方官,陆元荣.四元数在量子力学中的应用[J].大学物理, 2001,20(11):20-23.
[12] Liu Yusu, Zhang Xiuping. Some properties on quaternionic matrices[J]. Journal of Beijing Normal University, 2015,4(2):5-18.
[13]黄礼平.四元数矩阵的特征值与奇异值估计[J]. Journal of Mathematical Research with Applications, 1992,12(3):449-454.
[14] Zhang F. Gerschgorin type theorems for quaternionic matrices[J]. Linear Algebra&Its Applications, 2007,424(1):139-153.
[14] Wu J L. Distribution and estimation for eigenvalues of real quaternion matrices[J]. Computers&Mathematics with Applications, 2008,55(9):1998-2004.
[16]李文亮.四元数矩阵[M].长沙:国防科技大学出版社, 2002.
[17]邓勇,黄敬频.四元数体上一类矩阵方程解的数值方法[J].纯粹数学与应用数学, 2010,26(5):705-709.
[18] Zou L, Jiang Y, Wu J. Location for the right eigenvalues of quaternion matrices[J]. Journal of Applied Mathematics&Computing, 2012,38(1-2):71-83.