# What dose “Rank-two Modification w.r.t Matrix” Mean?

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?

-
This is illustrated here: en.wikipedia.org/wiki/Woodbury_matrix_identity – Steve Huntsman Oct 16 '12 at 20:07

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