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On the Rank of the Sum of two Rectangular Matrices

Published online by Cambridge University Press:  20 November 2018

C.D. Meyer
C.D. Meyer*
Affiliation:
North Carolina State University
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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,

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 12 , Issue 4 , August 1969 , pp. 508
Copyright
Copyright © Canadian Mathematical Society 1969

References

1. Penrose, R., A generalized inverse for matrices. Proc. Cambridge Philos. Soc. 51 (1955) 406–413.Google Scholar