Some linear transformations are adopt in the study of nonnegative-matrix and Z-matrix, and some properties are kept unvarying (for example spectral, trace of matrix).

• 摘要在对非负矩阵和Z-矩阵研究时，必要的方法是对它们进行变换、简化，同时这些变换常常要求必须保持矩阵一些性质（如矩阵谱迹等）不变。