Under multiplication, rows go into columns and all that. So if we transpose things, rows are being dot-producted with (what were originally) rows: [ a b ] [

Under multiplication, rows go into columns and all that. So if we transpose things, rows are being dot-producted with (what were originally) rows: [ a b ] [ a c ] = [ (a b) . (a b) (a b) . (c d) ] = [ |(a b)]^2 (a b) . (c d) ] [ c d ] [ b d ] [ (c d) . (a b) (c d) . (c d) ] [ (c d) . (a b) |(c d)|^2 ] Down the diagonal we have squared norms of (a b) and (c d) which is interesting and could somehow be used. We also have repeated values between the upper and lower triangle because (a b) . (c d) is the same as (c d) . (a b): the dot product commutes. Whereas just squaring the matrix: [ a b ] [ a b ] = [ (a b) . (a c) (a b) . (b d) ] [ c d ] [ c d ] [ (c d) . (a c) (c d) . (b d) ] all four dot products are unique. So right of the bat, we can find interesting things about X X^t without going deep, and an obvious shortcut.