Abstract
In this paper, algorithms for computing Jordan Normal Forms of square matrices over the rational number field are elucidated. The computation is exactly carried out by computer algebra, and the result is free from any numerical errors. These algorithms are deduced from well-known mathematical theorems, but they have not been installed yet in most of computer algebra system. Basic algorithms contain the step of solution of algebraic equations, which limits the applicability of the program. Theorefore, the improvement of the defect is discussed. The result of experimental implementation on REDUCE3.3 shows that the improved algorithm works quite efficiently.
