Some well-known results for matrices over a principal ideal domain are generalized to matrices over a Dedekind domain:
- necessary and sufficient conditions are obtained for a matrix to be diagonalizable and an algorithm is given to execute this diagonalization;
- the class of von Neumann regular matrices is characterized.
It is shown how to diagonalize a matrix of which it was known in literature that is was diagonalizable, but for which no constructive way was available to achieve the diagonalization. Also, an answer is given to question formulated by Den Boer.
Relations to results of L. Gerstein and M. Newman and to the calculation of the Moore-Penrose inverse of a matrix are mentioned.