### BENTUK NORMAL SMITH DAN MATRIKS BAIK KIRI/KANAN

#### Abstract

*The Smith normal form and left good matrix have been known in matrix theorem. Any matrix over the principal ideal ring has a Smith normal form. The Smith normal form of a matrix has many applications on various fields such as a solution of Diophantin linear equation and differential equation system. Furthermore, a matrix A with entries in a commutative ring R with unity is left good if for every vector x, the ideal **á**xA**ñ** is the same as the ideal **á**A**ñ**. This paper discusses the relation between the Smith normal form and left good matrix. The relation is as the following: matrix A with entries in principal ideal ring of size m by n, with *

*m **<** n, has Smith normal form [I _{m}, O] if only if A is a left good matrix.*

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PDF#### References

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