Abstract:

We gave the equivalent canonical form of a upper triangular matrix over a field. As applications, we proved that a upper triangular rankr matrix could be decomposed into a sum of finitely many upper triangular ranks matrices; we also proved that each ideal of the ring of all upper triangular matrices over a field was a principal ideal, which was generated by a unique reduced canonical upper triangular matrix.

Key words: upper triangular matrix, equivalent canonical form, rank, ideal