BENTUK NORMAL SMITH DAN MATRIKS BAIK KIRI / KANAN

NOVITASARI, LAILY (2009) BENTUK NORMAL SMITH DAN MATRIKS BAIK KIRI / KANAN. Other thesis, University of Muhammadiyah Malang.

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Abstract

The smith normal form and left good matrix have been known in matrix teorem. Any matriks 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 Diaphantin linier equation and differential equation system. Furthermore, a matrix A with entries in a commutative ring R with unity is left good matrix if for every vector x , the ideal xA is the same as the ideal A . this paper discusses left good matrikx and the relation between the Smith normal form and left good matrix. Since, for any matrix A and vector x , it is obvious that x xA ⊆ , the content of left good matrix is in the reverse containment. The relation is as the following: matrix A with entries in principal ideal ring of size m by n, with n m < , has Smith normal form ] 0 , [ m I if only if A is a left good matrix

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