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

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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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     title = {On the {Rank} of the {Sum} of two {Rectangular} {Matrices}},
     journal = {Canadian mathematical bulletin},
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     year = {1969},
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