## A basic decomposition result related to the notion of the rank of a matrix and applications.(English)Zbl 1084.15500

Summary: In this paper we present a basic decomposition theorem for matrices of rank $$r$$. Then we use this result to establish interesting properties and other results regarding the notion of rank of a matrix.

### MSC:

 15A21 Canonical forms, reductions, classification 15A23 Factorization of matrices

### Keywords:

rank of a matrix; basic decomposition theorem
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