令https://bgk-photo.cdn.bcebos.com/63d9f2d3572c11dfd43d1142732762d0f603c2e7.jpg表示数域https://bgk-photo.cdn.bcebos.com/38dbb6fd5266d0163bd63049872bd40734fa3587.jpg上一切https://bgk-photo.cdn.bcebos.com/d833c895d143ad4b90e1e8a192025aafa50f0687.jpg阶矩阵所成的向量空间.取定https://bgk-photo.cdn.bcebos.com/79f0f736afc3793144a72848fbc4b74542a91187.jpg.对任意https://bgk-photo.cdn.bcebos.com/e850352ac65c1038e59260a3a2119313b17e89e7.jpg,定义https://bgk-photo.cdn.bcebos.com/060828381f30e924c86b32505c086e061c95f780.jpg.(i) 证明:https://bgk-photo.cdn.bcebos.com/a8ec8a13632762d076f10adeb0ec08fa503dc680.jpg是https://bgk-photo.cdn.bcebos.com/f11f3a292df5e0fe74f427604c6034a85fdf72e7.jpg到自身的线性映射.(ii) 证明: 对于任意,https://bgk-photo.cdn.bcebos.com/94cad1c8a786c9176fecfc58d93d70cf3ac757e7.jpg,https://bgk-photo.cdn.bcebos.com/c2cec3fdfc039245f45a4f6e9794a4c27c1e25e7.jpg