Inverse problem for symmetric $P$-symmetric matrices with a submatrix constraint
Li, Jiao-fen ; Hu, Xi-yan ; Zhang, Lei
Bull. Belg. Math. Soc. Simon Stevin, Tome 17 (2010) no. 1, p. 661-674 / Harvested from Project Euclid
For a fixed generalized reflection matrix $P$, i.e., $P^T=P, P^2= I$, and $P\neq \pm I$, then a matrix $A $ is called a symmetric $P$-symmetric matrix if $A=A^T$ and $(PA)^T=PA$. This paper is mainly concerned with finding the least squares symmetric $P$-symmetric solutions to the matrix inverse problem $AX=B$ with a submatrix constraint, where $X$ and $B$ are given matrices of suitable size. By applying the generalized singular value decomposition and the canonical correlation decomposition, an analytical expression of the least squares solutions is derived basing on the Projection Theorem in Hilbert inner products spaces. Moreover, in the corresponding solution set, the analytical expression of the unique minimum-norm solution is described in detail.
Publié le : 2010-08-15
Classification:  Inverse problem,  symmetric $P$-symmetric matrix,  least squares solutions,  generalized singular value decomposition,  canonical correlation decomposition,  15A57,  15A24
@article{1290608193,
     author = {Li, Jiao-fen and Hu, Xi-yan and Zhang, Lei},
     title = {Inverse problem for symmetric $P$-symmetric matrices with a submatrix constraint},
     journal = {Bull. Belg. Math. Soc. Simon Stevin},
     volume = {17},
     number = {1},
     year = {2010},
     pages = { 661-674},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1290608193}
}
Li, Jiao-fen; Hu, Xi-yan; Zhang, Lei. Inverse problem for symmetric $P$-symmetric matrices with a submatrix constraint. Bull. Belg. Math. Soc. Simon Stevin, Tome 17 (2010) no. 1, pp.  661-674. http://gdmltest.u-ga.fr/item/1290608193/