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On the Rank of the Sum of two Rectangular Matrices
Published online by Cambridge University Press: 20 November 2018
Extract
The purpose of this note is to present a short proof for the following theorem.
Let A and B be two complex m x n matrices. If B*A = 0 and AB* = 0 then rank(A + B) = rank(A) + rank(B).
Let A† and B† be the generalized inverses of A and B, respectively, in the sense of Penrose [ 1]. Now,
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