## How to multiply matrices

This is for my homies in maths class.

Mathematical matrices are blocks of numbers, arrayed in 2-D. (Higher-dimensional array-verbs are called tensors.)

1. Left “times” right equals target. Each entry in the target is the result of a series of +'s and ×'s along the red and blue. A long sum of pairwise products.

2. Your left hand goes across and your right hand goes up/down.
where
.
3. There need to be as many `abcdefg`'s as there are `1234567`'s or else the operation can't be done.
4. Also you can tell how big the output matrix will be. There can be three blue rows so the output has three rows. There can be four red columns so the output has four columns.
5. This is the “inner product” because multiplying vector-shaped blocks (tall blocks) like Aᵀ•B results in an equal or smaller sized output.

(There is also an “outer product" which is a different way of combining the info from the two matrices. That gives you an equal or larger shaped result when you multiply vector/list-shaped tall blocks A∧B.)
6. Try playing around with this one or that one.

Matrix multiplication is the simplest example of a linear operator, the broad class of which explains quantum mechanics and ODE’s. You can also apply different matrices at different points as in a vector field — on a flat surface or a curvy, holey surface.

115 notes

1. clazzjassicalrockhop reblogged this from isomorphismes
2. phantom-cosmonaut reblogged this from isomorphismes
3. lemy reblogged this from isomorphismes
4. inkburn reblogged this from proofmathisbeautiful
5. topsyturvyimagination reblogged this from proofmathisbeautiful and added:
Oh, look. Linear Algebra. -__-
6. jenineyee reblogged this from proofmathisbeautiful
7. tipsyturvy-notions reblogged this from demith and added:
LOL. I liked matrices in 8th grade. They were really easy and simple and fun. o_o
8. demith reblogged this from proofmathisbeautiful
9. exposingdeception reblogged this from proofmathisbeautiful and added:
I miss doing this.
10. huynhie reblogged this from proofmathisbeautiful
11. aquaticater reblogged this from proofmathisbeautiful
12. aileenacoustic reblogged this from proofmathisbeautiful
13. ligong reblogged this from proofmathisbeautiful
14. hiley-kiccups reblogged this from proofmathisbeautiful
15. rowbot-weisguy reblogged this from proofmathisbeautiful
16. athousandtinylives reblogged this from proofmathisbeautiful