Geodesic
On the Rank of the Sum of two Rectangular Matrices
Canadian mathematical bulletin, Tome 12 (1969) no. 4, p. 508

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

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, 
Meyer, C.D. On the Rank of the Sum of two Rectangular Matrices. Canadian mathematical bulletin, Tome 12 (1969) no. 4, p. 508. doi: 10.4153/CMB-1969-065-0
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[1] 1. Penrose, R., A generalized inverse for matrices. Proc. Cambridge Philos. Soc. 51 (1955) 406–413. Google Scholar

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