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| In this paper focuses on the nonlinear quadratic matrix equation (AX2+BX, Y)=(C, X2), the existence range of solutions for a class of nonlinear matrix equations is derived by using the canonical correlation decomposition (CCD) of matrix pairs. When the rank of given coefficient matrix is equal to that of matrix pairs, the rank of matrix is unequal, and the rank of matrix column is full, the known matrix is mined by canonical correlation decomposition of matrix and basic elementary transformation of matrix. The relation between matrix and unknown matrix, the range of solutions of non-linear matrix equations, and the solution set of the problem are derived. |
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| Keywords:The nonlinear matrix equation,The canonical correlations decomposition,generalized
inverse. |
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