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I don't think I've seen the dot product there. Don't just throw terms around, it's very confusing for beginners :-). While I may have missed your idea about the
by weland 13y ago
I don't think I've seen the dot product there. Don't just throw terms around, it's very confusing for beginners :-). While I may have missed your idea about the dot product, I'm quite sure you can't express a dot product as a matrix multiplication; perhaps you were thinking you can express matrix multiplication in terms of dot products, but I don't see how that answer's OP's question.
- dbaupp 13y agoA 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 agoThat 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.
- alexchamberlain 13y agoIn all fairness, I misread the article. However, dot product is a very basic mathematical concept all readers of Hacker News should be aware of. Again, expressing the dot product as a matrix multiplication is basic linear algebra.