Re: History of Matrix Math



On Jan 26, 11:06 am, jdo...@xxxxxxxxx (James Dolan) wrote:

i don't know anything about the use of matrixes in weaving but i'd be
interested to learn about it because what you're describing sounds
like it might be interesting. however i just discovered that it's a
bit tricky to separate out the relevant results from the irrelevant
when feeding the terms "matrix" and "weaving" into a search engine.
could you (or someone) explain a bit about how matrixes are used in
weaving?



Hi jdo. I'll explain a bit...

We start with just a 4-shaft loom. Every warp thread passes through a
heddle fixed onto one and only one of these four shafts. So each thread
can be represented by a vector (1000),(0100),(0010),(0001).

Since the threads line up across the loom, we can use the vectors above
to create a matrix that represents all of the warp threads. We
translate the 4x1 vectors into 1x4 vectors, then put them side-by-side,
as in the 7-thread sample below:

0001000
0010100
0100010
1000001

Now when the weaver weaves (whether lamms, treadles, harnesses, or
whatever come into play as another poster noted), what is essentially
happening is that a shedd is formed by some combination of the shafts
rising and the remainder of the four shafts lowering.

So for four shafts, two outcomes, there are 16 possible shedds. But of
course all up or all down is no good for then there is no shed. So
that leaves 14, which can be represented by the vectors

(1110),(1101),(1011),(0111),(1010),(0101),(1100),(0110),(0011),(1001),(0001),(001:0),(0100),(1000)

So the treadling sequence is a combination of these 14 possibilities,
which again can be listed into a matrix.

So if you do matrix multiplication of the 7X4 threading matrix, and the
4x7(necessarily) treadling matrix, then the result represents the cloth
so woven.

I can say lots more about all of this if you're interested,

Bonnie.

.