J4 ›› 2012, Vol. 47 ›› Issue (4): 121-126.

• Articles • Previous Articles    

The least-squares solutions and the optimal approximation of the inverse problem for row anti-symmetric matrices on linear manifolds

LIANG Mao-lin, DAI Li-fang, YANG Xiao-ya   

  1. School of Mathematics and Statistics, Tianshui Normal University, Tianshui 741001,  Gansu, China
  • Received:2011-07-06 Online:2012-04-20 Published:2012-06-28

Abstract:

The least-squares row anti-symmetric solutions of matrix equations AX=B, XC=D on linear manifolds are obtained by using the singular value decomposition. Also, for a given matrix , the unique optimal approximation solution in the least-squares solutions set is derived.

Key words: matrix equations; least-squares solution; row anti-symmetric matrix; singular value decomposition; optimal approximation

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