On Linear Matrix Equations
Canadian mathematical bulletin, Tome 23 (1980) no. 1, pp. 43-49

Voir la notice de l'article provenant de la source Cambridge University Press

Some results from the theory of minimization of vector quadratic forms (subjected to linear restrictions) are used to obtain particular solutions to the usual types of linear matrix equations. An answer to a question raised by Greville [1] is supplied.
Scobey, P.; Kabe, D.G. On Linear Matrix Equations. Canadian mathematical bulletin, Tome 23 (1980) no. 1, pp. 43-49. doi: 10.4153/CMB-1980-006-4
@article{10_4153_CMB_1980_006_4,
     author = {Scobey, P. and Kabe, D.G.},
     title = {On {Linear} {Matrix} {Equations}},
     journal = {Canadian mathematical bulletin},
     pages = {43--49},
     year = {1980},
     volume = {23},
     number = {1},
     doi = {10.4153/CMB-1980-006-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1980-006-4/}
}
TY  - JOUR
AU  - Scobey, P.
AU  - Kabe, D.G.
TI  - On Linear Matrix Equations
JO  - Canadian mathematical bulletin
PY  - 1980
SP  - 43
EP  - 49
VL  - 23
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1980-006-4/
DO  - 10.4153/CMB-1980-006-4
ID  - 10_4153_CMB_1980_006_4
ER  - 
%0 Journal Article
%A Scobey, P.
%A Kabe, D.G.
%T On Linear Matrix Equations
%J Canadian mathematical bulletin
%D 1980
%P 43-49
%V 23
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1980-006-4/
%R 10.4153/CMB-1980-006-4
%F 10_4153_CMB_1980_006_4

[1] 1. Greville, T. N. E., Solution of the matrix equation XAX = X and relations between oblique and orthogonal projectors, SIAM J. Appl. Math., 26 (1974), 828-834. Google Scholar

[2] 2. Kabe, D. G., Minima of vector quadratic forms with applications to statistics, Metrika 12 (1968), 155-160. Google Scholar

[3] 3. Khatri, C. G. and Mitra, S. K., Hermitian and nonnegative definite solutions of linear matrix equations, SIAM J. Appl. Math., 31 (1976), 579-585. Google Scholar

[4] 4. Mitra, S. K., Fixed rank solutions to linear matrix equations, Sankhya Ser. A, 35 (1972), 387-392. Google Scholar

[5] 5. Mitra, S. K., Common solutions to a pair of matrix equations, AXB = Cx, AXB= C, Proc. Cambridge Phil. Soc, 74, (1973), 213-216. Google Scholar

[6] 6. Mitra, S. K., The matrix equation AXB + CXD = E, SIAM J. Appl. Math. 32 (1977), 823-825. Google Scholar

[7] 7. Rao, C. R., Estimation of variance and covariance components in linear models, J. Amer, Statisti. Assoc., 67 (1972), 112-115. Google Scholar

Cité par Sources :