The Minimal Norm Least Squares Solutions for a Class of Matrix Equations

Volume 7, Issue 6, December 2022     |     PP. 132-138      |     PDF (210 K)    |     Pub. Date: December 11, 2022
DOI: 10.54647/mathematics11371    74 Downloads     2459 Views  

Author(s)

Jinrong Shen, College of Mathematics, Changsha University, Changsha 410003, China

Abstract
In this paper, the minimal norm least squares solution of matrix equations (AXC,BXD,AXD,BXC)=(E,F,G,H) is discussed, by using the projection theorem, the generalized singular value decomposition and the canonical correlation decomposition, the expression of the solution of this problem is obtained.

Keywords
Minium-norm least-square solution; the Generalized Singular Value Decomposition; the Canonical Correlation Decomposition; the Projection Theorem

Cite this paper
Jinrong Shen, The Minimal Norm Least Squares Solutions for a Class of Matrix Equations , SCIREA Journal of Mathematics. Volume 7, Issue 6, December 2022 | PP. 132-138. 10.54647/mathematics11371

References

[ 1 ] Chen X T. Common solutions of a class of matrix equations. Numerical Mathematics A Journal of Chinese. 2005, 27(2):133-148.
[ 2 ] X.Yuan. On the two class of best approximation problems. Math.Numerica Sinica. 2001, 23:429-436.
[ 3 ] H.Golub, C.F.Van Loan. Matrix Computations. The Johns Hopkins Univ Press, Baltimore, MD, 1997.
[ 4 ] G.W.Setward, J.G.Sun. Matrix Perturbation Theory. Academic Press, New York,1990. 1998, 279:93-109.
[ 5 ] R.S.Wang. Functional Analysis and Optimization Theory. Beijing University of Aeronautics & Astronautics Press ,Beijing, 2003.
[ 6 ] Golub G H, Vanloan C F. Matrix Computation. Baltimore: Johns Hopkins University Press, 1996, 53-644.
[ 7 ] Liao A P, Lei Y, Yuan S F. The matrix nearness problem for symmetric matrices associated with the matrix equation [ATXA,BTXB]=[C,D]. Linear Algebra and Its Applications, 2006, 418: 939-954.
[ 8 ] Zhang S B, Deng Y. Reflexive solutions and antireflexive solutions of matrix equation AXB+CYD=E. Journal of Northeast Normal University (Natural Science Edition). 2022, 54(02):1-4.
[ 9 ] Ma Y, Huang X F. The solution of inverse Hermite matrix equation. University Mathematics. 2022,38(04):121-124.