2 ms·

A conventional (i.e. with vectors over ℝ) dot product is just a matrix multiplication between a 1×n and an n×1 matrix.

• weland 13y ago
  That hardly qualifies as "you can express dot product as matrix multiplication" in the context of the discussion about complexity. I also think it's backwards from a theoretical standpoint. Dot product isn't a cornercase of matrix multiplication, it has a meaning of its own that can be viewed without even introducing matrices. You can view matrix multiplication as computationally equivalent with a sequence of dot products, but that where stuff ends; otherwise, for instance, matrix multiplication also doesn't have all the properties that the dot product has (e.g. it's not commutative). I know a lot of books take this shortcut, but the two concepts are different enough that, IMO, they do not warrant alexchamberlain's remark.