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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
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