On solutions of the matrix equation X A_0=A_1 with prescribed characteristic polynomials
DOI:
https://doi.org/10.15673/2072-9812.4/2014.41436Keywords:
Matrix linear equation, Characteristic polynomialAbstract
We investigate the structure of solutions of a matrix equation X A0=A1, where A0, A1 are (nxm) matrices over a field F and X is unknown (nxm) matrix. Let
d(λ) = λn+d1 λn-1+…dn-1 λ+dn ∈ F[λ] be a monic polynomial of degree n. In this note we present the conditions under which for the equation X A0=A1 there exists a solution X0=D with the characteristic polynomial d(λ).
References
Ф.Р. Гантмахер. Теория матриц. М.: Физматлит, 1988, 556 с.
F.J.H. Don. On the symmetric solutions of a linear matrix equation
// Linear Algebra Appl., 93(1987), p.1–7.
K.-W.E. Chu. Symmetric solutions of linear matrix equations by matrix decom-positions // Linear Algebra Appl., 119 (1989), p.35–50.
Hua Dai. On the symmetric solutions of linear matrix equations // Linear Algebra Appl., 131 (1990), p.1–7.
L. Wu. The Re-positive definite solution to the matrix inverse problem AX=B // Linear Algebra Appl., 174 (1992), p.145–151.
L. Wu, B. Cain. The Re-nonnegative definite solutions to the matrix inverse problem AX=B // Linear Algebra Appl., 236 (1996), p.137–146.
Zhenyun Peng, Xiyan Hu. The reflexive and anti-reflexive solutions of the matrix equation AX=B // Linear Algebra Appl., 375 (2003), p.147–155.
Chunjun Meng, Xiyan Hu, Lei Zhang. The skew-symmetric orthogonal solutions of the matrix equation AX=B // Linear Algebra Appl., 402 (2005), p.303–318.
R.A. Horn, V. Sergeichuk, N. Shaked-Monderer. Solution of linear matrix equa-tions in a *congruence class // Electron. J. Linear Algebra, 17 (2005), p.153–156.
Bing Zheng, Lijuan Ye, Dragana S. Cvetkovic-Ilic. The *congruence class of the solutions of some matrix equations // Comput. Math. Appl., 57 (2009), p.540-549.
