Incoherence property in Matrix Completion I'm not a math major and I find the statement below confusing (from a paper by Candes and Recht on Matrix Completion). Can someone clarify this? I'm sure it's painfully simple/obvious. > "For instance, consider the rank-2 symmetric matrix M given by > > !enter image description here > > where the singular values are arbitrary. Then this matrix vanishes everywhere except in the top left 2x2 corner." I'm taking e1 and e2 as [1 0] and [0 1], respectively. It's confusing to me because it seems that M was never any bigger than 2x2. So why would they say it vanishes everywhere except in the 2x2 left-uppermost corner?

You want $$ e_1 = [1, 0, 0, 0, \cdots 0] \\\ e_2 = [0,1,0,0, \cdots 0] $$

If each vector is $n$ long you will end up with a $n\times n$ matrix with just two entries as stated.