philh comments on Stupid Questions September 2016 - Less Wrong

3 Post author: pepe_prime 05 September 2016 10:34PM

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Comment author: DataPacRat 10 September 2016 02:30:07AM 3 points [-]

Matrix multiplication

Could somebody explain to me, in a way I'd actually understand, how to (remember how to) go about multiplying a pair of matrixes? I've looked at Wikipedia, I've read linear algebra books up to where they supposedly explain matrixes, and I keep bouncing up against a mental wall where I can't seem to remember how to figure out how to get the answer.

Comment author: philh 12 September 2016 10:44:49AM *  3 points [-]

Low confidence that this will help, but my approach: I mentally move the right-hand matrix up, so that the space "in between" them (right of the first, below the second) is the right shape for the result. Each value of the result is the dot product of the vectors to the left and above it. (I don't have a trick for dot products, I just know how to calculate them.)

. . . . g h i
a b c * j k l
d e f . m n o

"becomes"

. . . g h i
. . . j k l
. . . m n o
. . . -----
a b c|S T W
d e f|X Y Z

and e.g. S is (a b c) dot (g j m), Y is (d e f) dot (h k n).

Comment author: Viliam 12 September 2016 04:04:17PM 0 points [-]

I use exactly the same approach! When you position the matrices this way, it becomes completely obvious.

Comment author: DataPacRat 12 September 2016 10:19:31PM 2 points [-]

By Juniper, I think this is the one. It's simple enough that I can actually remember this, and I can solve arbitrary matrixes with this approach.

Feel free to have an internet cookie in thanks. :)

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