Geodesic
When Does Rank(A+B)=Rank(A)+Rank(B)?
Canadian mathematical bulletin, Tome 15 (1972) no. 3, pp. 451-452

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

In a recent note in the Bulletin, Murphy [5] gave a short proof that for complex m×n matrices A and B, r(A+B)=r(A)+r(B) if the rows of A are orthogonal to the rows of B and the columns of A are orthogonal to the columns of B. His proof was elegant and simple, an improvement on an earlier proof of the same result by Meyer [4]. 
Marsaglia, G.; Styan, G. P. H. When Does Rank(A+B)=Rank(A)+Rank(B)?. Canadian mathematical bulletin, Tome 15 (1972) no. 3, pp. 451-452. doi: 10.4153/CMB-1972-082-8
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[1] 1. Khatri, C. G., A simplified approach to the derivation of the theorems on the rank of a matrix, J. Maharaja Sayajirao Univ. Baroda, 10 (1961), 1-5. Google Scholar

[2] 2. George, Marsaglia, Bounds on the rank of the sum of matrices, Trans, of the Fourth Prague Conf. on Information Theory, Statistical Decision Functions, Random Processes (Prague, August 31-Sept. 11, 1965), Czechoslovak Acad. Sci. (1967), 455-462. Google Scholar

[3] 3. George, Marsaglia and Styan, George P. H., Inequalities and equalities for ranks of matrices (to appear). Google Scholar

[4] 4. Meyer, C. D., On the rank of the sum of two rectangular matrices, Canad. Math. Bull. 12 (1969), p. 508. Google Scholar

[5] 5. Ian S., Murphy, The rank of the sum of two rectangular matrices, Canad. Math. Bull. 13 (1970), p. 384. Google Scholar

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