Geodesic
Invariant Factors Under Rank One Perturbations
Canadian journal of mathematics, Tome 32 (1980) no. 1, pp. 240-245

Voir la notice de l'article provenant de la source Cambridge University Press

Let R be a principal ideal domain, i.e., a commutative ring without zero divisors in which every ideal is principal. The invariant factors of a matrix A with entries in R are the diagonal elements when A is converted to a diagonal form D = UAV, where U, V have entries in R and are unimodular (invertible over R), and the diagonal entries d1 ..., dn of D form a divisibility chain: d1|d2| ... |dn. Very little has been proved about how invariant factors may change when matrices are added. This is in contrast to the corresponding question for matrix multiplication, where much information is now available [6]. 
Thompson, Robert C. Invariant Factors Under Rank One Perturbations. Canadian journal of mathematics, Tome 32 (1980) no. 1, pp. 240-245. doi: 10.4153/CJM-1980-018-9
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