id: 06169915
dt: j
an: 06169915
au: Wang, Qing-Wen; Yu, Juan
ti: Constrained solutions of a system of matrix equations.
so: J. Appl. Math. 2012, Article ID 471573, 19 p. (2012).
py: 2012
pu: Hindawi, New York, NY
la: EN
cc:
ut: orthogonal solutions; symmetric orthogonal solutions; skew-symmetric
orthogonal solutions; system of matrix equations; least squares
symmetric orthogonal solutions; least squares skew-symmetric orthogonal
solutions; algorithm
ci:
li: doi:10.1155/2012/471573
ab: Summary: We derive necessary and sufficient conditions and the expressions
for the orthogonal solutions, the symmetric orthogonal solutions, and
the skew-symmetric orthogonal solutions of the system of matrix
equations $AX = B$ and $XC = D$, respectively. When the matrix
equations are not consistent, the least squares symmetric orthogonal
solutions and the least squares skew-symmetric orthogonal solutions are
respectively given. As an auxiliary, an algorithm is provided to
compute the least squares symmetric orthogonal solutions, and meanwhile
an example is presented to show that it is reasonable.
rv: