刻画了$2\times 2$无界奇异\hspace*{-1.5pt}$\mathcal{J}$-自伴算子矩阵的可逆性, 并且得到相应的缺项算子矩阵存在可逆补的充分必要条件, 最后举例验证了结果的合理性.

The invertibility of unbounded singular $\mathcal{J}$-self-adjoint operator matrices is characterized, and the necessary and sufficient condition for certain partial operator matrices to exist invertible completion is further obtained. Moreover, some concrete examples are presented to illustrate the results.