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The Research on the Problems of Integer MatrixKeywords: integer matrix;similarity;diagonalization , eigenvalue , eigenvector Abstract: 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.
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