The general solution of Non-linear Matrix Equation
Changqing Xu · Journal of Guangxi University · 2008
The general solution of solvable matrix equation Xm=A was obtained.If A is non-singular matrix,the equation Xm=A has finitely many solutions.Specially,the number of the m-root of non-singular Jordan block was m.When the matrix is a singular matrix,it may have m-root,also possible have no m-root.This is determined by their Jordan normal form.And when m is an even number,the solutions of Xm=A span whole Cn×nif and only if A=λI withλ≠0.We also determine the precise number of solutions in various cases.