Abstract
By applying the methods presented by Yuan et al. [Yuan, S.F., Wang, Q.W.: Two special kinds of least squares solutions for the quaternion matrix equation AXB + CXD = E. Electron. J. Linear Algebra 23, pp. 257–274 (2012)], we derive the expression of the least squares η -Hermitian solution of the quaternion matrix equation AXB = C with the least norm.
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References
Took, C.C., Mandic, D.P., Zhang, F.Z.: On the unitary diagonalisation of a special class of quaternion matrices. Appl. Math. Lett. 24, 1806–1809 (2011)
Huang, L.P.: The matrix equation AXB-CXD=E over the quaternion field. Linear Algebra Appl. 234, 197–208 (1996)
Jiang, T.S., Wei, M.S.: On a solution of the quaternion matrix equation X-AXB=C and its application. Acta Math. Sin. 21, 483–490 (2005)
Li, Y.T., Wu, W.J.: Symmetric and skew-antisymmetric solutions to systems of real quaternion matrix equations. Comput. Math. Applic. 55, 1142–1147 (2008)
Yuan, S.F., Liao, A.P., Lei, Y.: Minimization problem for Hermitian matrices over the quaternion field. Acta Math. Sci. 29A, 1298–1306 (2009) (in Chinese)
Yuan, S.F., Liao, A.P.: Least squares solution of quaternion matrix equation with the least norm. Linear Multilinear Algebra 59(9), 985–998 (2011)
Yuan, S.F., Liao, A.P., Duan, X.F.: Least squares tridiagonal Hermitian solution and tridiagonal bi-Hermitian solution of the quaternion matrix equation AXB=C with the least norm. Numerical Mathematics A Journal of Chinese Universities 32(4), 353–368 (2010)
Yuan, S.F., Liao, A.P., Yao, G.Z.: The matrix nearness problem associated with the quaternion matrix equation AXA H + BYB H =C. J. Appl. Math. Comput. 37, 133–144 (2011)
Took, C.C., Mandic, D.P.: Augmented second-order statistics of quaternion random signals. Signal Processing 91, 214–224 (2011)
Ell, T., Sangwine, S.J.: Quaternion involutions and anti-involutions. Comput. Math. Applic. 53, 137–143 (2007)
Yuan, S.F., Liao, A.P., Lei, Y.: Least squares Hermitian solution of the matrix equation (AXB,CXD)=(E,F) with the least norm over the skew field of quaternions. Math. Comput. Modelling 48, 91–100 (2008)
Yuan, S.F., Wang, Q.W.: Two special kinds of least squares solutions for the quaternion matrix equation AXB+CXD=E Electron. J. Linear Algebra 23, 257–274 (2012)
Magnus, J.R.: L-structured matrices and linear matrix equations. Linear Multilinear Algebra 14, 67–88 (1983)
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Yuan, S. (2012). Least Squares η - Hermitian Solution for Quaternion Matrix Equation AXB = C . In: Liu, C., Wang, L., Yang, A. (eds) Information Computing and Applications. ICICA 2012. Communications in Computer and Information Science, vol 307. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34038-3_41
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DOI: https://doi.org/10.1007/978-3-642-34038-3_41
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