The Research on the Problems of Integer Matrix

Because the element on the metal ring may not have the inverse, so the theorems on the matrix in field would perhaps incorrect. In this article, I mainly do research on the eigenvalue, eigenvector and similar diagonalization. These results are: integer matrix can change into upper triangular matrix through integer elementary row operation; two necessary and sufficient conditions about similarity diagonalization of integer matrix; if the integer matrix has different eigenvalue, it can diagonalizable if and only if it is an integer diagonal matrix.