Journal of East China Normal University(Natural Sc ›› 2009, Vol. 2009 ›› Issue (4): 39-46.

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Algebraic method for least squares problems in quaternionic quantum theory

LING Si-tao$^{1, 2}$, JIANG Tong-song$^2$, WEI Mu-sheng$^{1, 3}

  

  1. 1. {\it Department of Mathematics, East China Normal University, Shanghai} 200241, {\it China};} \DWEI{2. {\it Department of Mathematics, Linyi Normal University, Linyi Shandong} 276005, {\it China};} \DWEI{3. {\it Department of Mathematics, Shanghai Normal University, Shanghai} 200234
  • Received:2008-09-06 Revised:2008-12-06 Online:2009-07-25 Published:2009-07-25
  • Contact: WEI Mu-sheng

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Abstract: This paper introduced concepts of norms of quaternion matrices by means of
complex representation of a quaternion matrix, studied the quaternionic least squares
(QLS) problem and derived an algebraic method of finding solutions of the QLS problem in
quaternionic quantum theory. A numerical example verified the efficiency of the
algorithm.

Key words: complex representation, normal equation , quaternionic least squares, complex representation, normal equation

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