Linear Algebra Toolkit

http://www.math.odu.edu/~bogacki/lat/

This looks really useful. Gene, can you please

show me by example how to use it? How about if we

examine the Schoenberg unison-vector matrix I posted

yesterday?

2 3 5 7 11 unison vectors ~cents

[ 11 -4 -2 0 0] = 2048:2025 19.55256881

[ -5 1 0 0 1] = 33:32 53.27294323

[ 6 -2 0 -1 0] = 64:63 27.2640918

[ -4 4 -1 0 0] = 81:80 21.5062896

inverse (without powers of 2) =

[-1 0 0 2]

[-4 0 0 -4] 1

[ 2 0 -12 -4] * --

[ 1 12 0 -2] 12

-monz

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--- In tuning-math@y..., "monz" <joemonz@y...> wrote:

> 2 3 5 7 11 unison vectors ~cents

>

> [ 11 -4 -2 0 0] = 2048:2025 19.55256881

> [ -5 1 0 0 1] = 33:32 53.27294323

> [ 6 -2 0 -1 0] = 64:63 27.2640918

> [ -4 4 -1 0 0] = 81:80 21.5062896

I went to the "finding the null space" module, and told it to give me four rows and five columns, and then inputted the above. It tells me the solution is

[12/41]

[19/41]

[28/41]

[34/41]

[1 ]

Multiplying through by 41, I find that the corresponding val is

[12]

[19]

[28]

[34]

[41]