A. Dajic and J. J. Koliha, “Equations ax = c and xb = b in Rings and Rings with Involution with Applications to Hilbert Space Operators,” Linear Algebra and Its Applications, Vol. 429, No. 7, 2008, pp. 1779-1809. doi10.1016/j.laa.2008.05.012 - References

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A. Dajic and J. J. Koliha, “Equations ax = c and xb = b in Rings and Rings with Involution with Applications to Hilbert Space Operators,” Linear Algebra and Its Applications, Vol. 429, No. 7, 2008, pp. 1779-1809. doi:10.1016/j.laa.2008.05.012

has been cited by the following article:

TITLE: Least Squares Symmetrizable Solutions for a Class of Matrix Equations

AUTHORS: Fanliang Li

KEYWORDS: Matrix Equations; Matrix Row Stacking; Topological Isomorphism; Least Squares Solution; Optimal Approximation

JOURNAL NAME: Applied Mathematics, Vol.4 No.5, May 13, 2013

ABSTRACT: In this paper, we discuss least squares symmetrizable solutions of matrix equations (AX = B, XC = D) and its optimal approximation solution. With the matrix row stacking, Kronecker product and special relations between two linear subspaces are topological isomorphism, and we derive the general solutions of least squares problem. With the invariance of the Frobenius norm under orthogonal transformations, we obtain the unique solution of optimal approximation problem. In addition, we present an algorithm and numerical experiment to obtain the optimal approximation solution.