Douglas Blumeyer's RTT How-To: Difference between revisions

Line 588:

And ta-da! You’ve found the mapping for which the comma basis we started with is a basis for the null-space, and it is {{monzo|{{val|19 30 44}}}}. Feel free to try this with any other combination of two commas tempered out by this map.

{| class="wikitable"

|+WolframAlpha code ([https://www.wolframalpha.com/input/?i=basis+of+NullSpace%5B%7B%7B-1%2C4%2C-4%7D%2C%7B5%2C-1%2C-10%7D%7D%5D try it])

!input

!output

|-

|<code>basis of NullSpace[{{-1,4,-4},{5,-1,-10}}]</code>

|{44,30,19}

|}

Now the null-space function, to take you from {{monzo|{{val|19 30 44}}}} back to the matrix, is pretty much the same thing, but a bit simpler. No need to transpose or reverse. Just start at the augmentation step:

Line 655:

Line 664:

So that’s not any of the commas we’ve looked at so far (it’s the [[19-comma]] and the [[acute limma]]). But it is clear to see that either of them would be tempered out by 19-ET (no need to map by hand — just look at these commas side-by-side with the map {{monzo|{{val|19 30 44}}}} and it should be apparent).

Null-space can be calculated by specialized math programs and web tools. But I think it’s a good idea to work through it by hand at least a couple times, to demystify it and give you a feel for it.

{| class="wikitable"

|+WolframAlpha code ([https://www.wolframalpha.com/input/?i=basis+of+NullSpace%5B%7B%7B19%2C30%2C44%7D%7D%5D try it])

!input

!output

|-

|<code>basis of NullSpace[<nowiki>{{19,30,44}}</nowiki>]</code>

|{{-44,0,19},{-30,19,0}}

|}

Null-space can be calculated by specialized math programs and web tools, as linked above. But I think it’s a good idea to work through it by hand at least a couple times, to demystify it and give you a feel for it.

=== the other side of duality ===

@@ Line 588: / Line 588: @@
 And ta-da! You’ve found the mapping for which the comma basis we started with is a basis for the null-space, and it is {{monzo|{{val|19 30 44}}}}. Feel free to try this with any other combination of two commas tempered out by this map.
+{| class="wikitable"
+|+WolframAlpha code ([https://www.wolframalpha.com/input/?i=basis+of+NullSpace%5B%7B%7B-1%2C4%2C-4%7D%2C%7B5%2C-1%2C-10%7D%7D%5D try it])
+!input
+!output
+|-
+|<code>basis of NullSpace[{{-1,4,-4},{5,-1,-10}}]</code>
+|{44,30,19}
+|}
 Now the null-space function, to take you from {{monzo|{{val|19 30 44}}}} back to the matrix, is pretty much the same thing, but a bit simpler. No need to transpose or reverse. Just start at the augmentation step:
@@ Line 655: / Line 664: @@
 So that’s not any of the commas we’ve looked at so far (it’s the [[19-comma]] and the [[acute limma]]). But it is clear to see that either of them would be tempered out by 19-ET (no need to map by hand — just look at these commas side-by-side with the map {{monzo|{{val|19 30 44}}}} and it should be apparent).
-Null-space can be calculated by specialized math programs and web tools. But I think it’s a good idea to work through it by hand at least a couple times, to demystify it and give you a feel for it.
+{| class="wikitable"
+|+WolframAlpha code ([https://www.wolframalpha.com/input/?i=basis+of+NullSpace%5B%7B%7B19%2C30%2C44%7D%7D%5D try it])
+!input
+!output
+|-
+|<code>basis of NullSpace[<nowiki>{{19,30,44}}</nowiki>]</code>
+|{{-44,0,19},{-30,19,0}}
+|}
+Null-space can be calculated by specialized math programs and web tools, as linked above. But I think it’s a good idea to work through it by hand at least a couple times, to demystify it and give you a feel for it.
 === the other side of duality ===