On Positive Definite Solutions of Quaternionic Matrix Equations
The real representation of the quaternionic matrix is
definited and studied. The relations between the positive (semi)define
quaternionic matrix and its real representation matrix are presented.
By means of the real representation, the relation between the positive
(semi)definite solutions of quaternionic matrix equations and those of
corresponding real matrix equations is established.
[1] D. Finkelstein , J. Jauch , S. Schiminovich and D. Speiser, Foundations of
quaternion quantum mechanics, J. Math. Phys., vol. 3, 1962, pp.207-231.
[2] S. Adler, Quaternionic quantum field theory Commun. Math. Phys., vol.
104, 1986, pp. 611-623.
[3] S. Adler, Quaternionic Quantum Mechanics and Quantum Fields, New
York: Oxford University Press, 1995.
[4] J. Jiang, An algorithm for quaternionic linear equations in quaternionic
quantum theory, J. Math. Phys., vol. 45, 2004, pp.4218-4228.
[5] J. Jiang, Cramer ruler for quaternionic linear equations in quaternionic
quantum theory, Rep. Math. Phys., vol. 57, 2006, pp. 463-467.
[6] J. Jiang, Algebraic algorithms for least squares problem in quaternionic
quantum theory, Comput. Phys. Commun., vol. 176, 2007, pp. 481-485.
[7] J. Jiang, Real representiations of quaternion matrices and quaternion
matrix equations, Acta Mathematica Scientia, vol. 26A, 2006, pp. 578-
584.
[8] M. Wang, M. Wei and Y. Feng, An iterative algorithm for least squares
problem in quaternionic quantum theory, Comput. Phys. Commun., vol.
179, 2008, pp. 203-207.
[1] D. Finkelstein , J. Jauch , S. Schiminovich and D. Speiser, Foundations of
quaternion quantum mechanics, J. Math. Phys., vol. 3, 1962, pp.207-231.
[2] S. Adler, Quaternionic quantum field theory Commun. Math. Phys., vol.
104, 1986, pp. 611-623.
[3] S. Adler, Quaternionic Quantum Mechanics and Quantum Fields, New
York: Oxford University Press, 1995.
[4] J. Jiang, An algorithm for quaternionic linear equations in quaternionic
quantum theory, J. Math. Phys., vol. 45, 2004, pp.4218-4228.
[5] J. Jiang, Cramer ruler for quaternionic linear equations in quaternionic
quantum theory, Rep. Math. Phys., vol. 57, 2006, pp. 463-467.
[6] J. Jiang, Algebraic algorithms for least squares problem in quaternionic
quantum theory, Comput. Phys. Commun., vol. 176, 2007, pp. 481-485.
[7] J. Jiang, Real representiations of quaternion matrices and quaternion
matrix equations, Acta Mathematica Scientia, vol. 26A, 2006, pp. 578-
584.
[8] M. Wang, M. Wei and Y. Feng, An iterative algorithm for least squares
problem in quaternionic quantum theory, Comput. Phys. Commun., vol.
179, 2008, pp. 203-207.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:53486", author = "Minghui Wang", title = "On Positive Definite Solutions of Quaternionic Matrix Equations", abstract = "The real representation of the quaternionic matrix is
definited and studied. The relations between the positive (semi)define
quaternionic matrix and its real representation matrix are presented.
By means of the real representation, the relation between the positive
(semi)definite solutions of quaternionic matrix equations and those of
corresponding real matrix equations is established.", keywords = "Matrix equation, Quaternionic matrix, Real representation,positive (semi)definite solutions.", volume = "4", number = "1", pages = "18-3", }