On the existence of a positive definite solution of the matrix equation X+AXA=I
On the existence of a positive definite solution of the matrix equation X+AXA=I
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发表时间：
1989
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通讯作者：
J. Engwerda
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作者：
J. Engwerda
本文讨论了在真实的T-1（平方）矩阵A上，矩阵方程XfAXA-I在什么条件下有真实的对称正定解X.给出了A上可解的充要条件。并给出了求解的算法。对于一些特殊情况，我们也提出了一个解析解。
In this paper the question is raised under which conditions on the real T -1 (square) matrix A, the matrix equation X f A X A- I has a real symmetric positive definite solution X. Both necessary and sufficient solvability conditions on A are derived. Moreover, we give an algorithm to calculate the solution. For a number of special cases we also present an analytic solution.