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I came over "rank-one modification of $A$", "rank-two modification of $B$" in my readings and want to know what does "rank-N modification" w,r,t a matrix mean?

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This is illustrated here: – Steve Huntsman Oct 16 '12 at 20:07

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A matrix $B$ is said to be a rank-$k$ modification of $A$ if $B-A$ has rank $k$ (or sometimes rank at most $k$).

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