Douglas Blumeyer's RTT How-To: Difference between revisions
Cmloegcmluin (talk | contribs) m →intersections and unions: add note from Keenan about trivial temperaments |
Cmloegcmluin (talk | contribs) m →null-space: colorize matrices for extra clarity |
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\left[ \begin{array} {rrr} | \left[ \begin{array} {rrr} | ||
-1 & 0 & 0 \\ | -1 & 0 & \color{lime}0 \\ | ||
5 & 19 & 0 \\ | 5 & 19 & \color{lime}0 \\ | ||
\hline | \hline | ||
1 & 4 & 44 \\ | 1 & 4 & \color{green}44 \\ | ||
0 & 1 & 30 \\ | 0 & 1 & \color{green}30 \\ | ||
0 & 0 & 19 | 0 & 0 & \color{green}19 | ||
\end{array} \right] | \end{array} \right] | ||
</math> | </math> | ||
| Line 554: | Line 554: | ||
<math> | <math> | ||
\left[ \begin{array} {rrr} | \left[ \begin{array} {rrr} | ||
44 \\ | \color{green}44 \\ | ||
30 \\ | \color{green}30 \\ | ||
19 | \color{green}19 | ||
\end{array} \right] | \end{array} \right] | ||
</math> | </math> | ||
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\left[ \begin{array} {rrr} | \left[ \begin{array} {rrr} | ||
19 & 570 & 0 \\ | 19 & 570 & \color{lime}0 \\ | ||
\hline | \hline | ||
1 & 0 & -44 \\ | 1 & 0 & \color{green}-44 \\ | ||
0 & 19 & 0 \\ | 0 & 19 & \color{green}0 \\ | ||
0 & 0 & 19 | 0 & 0 & \color{green}19 | ||
\end{array} \right] | \end{array} \right] | ||
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\left[ \begin{array} {rrr} | \left[ \begin{array} {rrr} | ||
19 & 0 & 0 \\ | 19 & \color{lime}0 & \color{lime}0 \\ | ||
\hline | \hline | ||
1 & -30 & -44 \\ | 1 & \color{green}-30 & \color{green}-44 \\ | ||
0 & 19 & 0 \\ | 0 & \color{green}19 & \color{green}0 \\ | ||
0 & 0 & 19 | 0 & \color{green}0 & \color{green}19 | ||
\end{array} \right] | \end{array} \right] | ||
</math> | </math> | ||
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<math> | <math> | ||
\left[ \begin{array} {rrr} | \left[ \begin{array} {rrr} | ||
-30 & -44 \\ | \color{green}-30 & \color{green}-44 \\ | ||
19 & 0 \\ | \color{green}19 & \color{green}0 \\ | ||
0 & 19 | \color{green}0 & \color{green}19 | ||
\end{array} \right] | \end{array} \right] | ||
</math> | </math> | ||
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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. | 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. | ||
=== the other side of duality === | === the other side of duality === | ||