Diamond tradeoff: Difference between revisions
Cmloegcmluin (talk | contribs) →Example: remove confusing and possibly wrong reference to pseudoinverse here, simplify MathJax format, and clarify cancelation step |
Cmloegcmluin (talk | contribs) →Example: better matrix formatting (in particular right-alignment) |
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| Line 30: | Line 30: | ||
<math> | <math> | ||
\begin{ | \left[ \begin{array} {rrr} | ||
1 & 0 & -4 \\ | 1 & 0 & -4 \\ | ||
0 & 1 & 4 \\ | 0 & 1 & 4 \\ | ||
\end{ | \end{array} \right] | ||
</math> | </math> | ||
| Line 43: | Line 43: | ||
<math> | <math> | ||
\begin{ | \left[ \begin{array} {rrr} | ||
1 & 2 \\ | 1 & 2 \\ | ||
0 & -1 \\ | 0 & -1 \\ | ||
0 & 0 \\ | 0 & 0 \\ | ||
\end{ | \end{array} \right] | ||
</math> | </math> | ||
| Line 63: | Line 63: | ||
<math> | <math> | ||
\begin{ | \left[ \begin{array} {rrr} | ||
1 & 0 & -4 \\ | 1 & 0 & -4 \\ | ||
0 & 1 & 4 \\ | 0 & 1 & 4 \\ | ||
\end{ | \end{array} \right] | ||
\begin{ | \left[ \begin{array} {rrr} | ||
1 & 2 \\ | 1 & 2 \\ | ||
0 & -1 \\ | 0 & -1 \\ | ||
0 & 0 \\ | 0 & 0 \\ | ||
\end{ | \end{array} \right] = | ||
\begin{ | \left[ \begin{array} {rrr} | ||
1 & 1 \\ | 1 & 1 \\ | ||
0 & -1 \\ | 0 & -1 \\ | ||
\end{ | \end{array} \right] | ||
</math> | </math> | ||
| Line 81: | Line 81: | ||
<math> | <math> | ||
\begin{ | \left[ \begin{array} {rrr} | ||
1 & 1 \\ | 1 & 1 \\ | ||
0 & -1 \\ | 0 & -1 \\ | ||
\end{ | \end{array} \right] | ||
</math> | </math> | ||
| Line 90: | Line 90: | ||
<math> | <math> | ||
\begin{ | \left[ \begin{array} {rrr} | ||
1 & 2 \\ | 1 & 2 \\ | ||
0 & -1 \\ | 0 & -1 \\ | ||
0 & 0 \\ | 0 & 0 \\ | ||
\end{ | \end{array} \right] | ||
\begin{ | \left[ \begin{array} {rrr} | ||
1 & 1 \\ | 1 & 1 \\ | ||
0 & -1 \\ | 0 & -1 \\ | ||
\end{ | \end{array} \right] = | ||
\begin{ | \left[ \begin{array} {rrr} | ||
1 & -1 \\ | 1 & -1 \\ | ||
0 & 1 \\ | 0 & 1 \\ | ||
0 & 0 \\ | 0 & 0 \\ | ||
\end{ | \end{array} \right] | ||
</math> | </math> | ||
| Line 111: | Line 111: | ||
<math> | <math> | ||
\begin{ | \left[ \begin{array} {rrr} | ||
1 & -2 \\ | 1 & -2 \\ | ||
0 & 0 \\ | 0 & 0 \\ | ||
0 & 1 \\ | 0 & 1 \\ | ||
\end{ | \end{array} \right] | ||
</math> | </math> | ||
| Line 121: | Line 121: | ||
<math> | <math> | ||
\begin{ | \left[ \begin{array} {rrr} | ||
1 & 0 & -4 \\ | 1 & 0 & -4 \\ | ||
0 & 1 & 4 \\ | 0 & 1 & 4 \\ | ||
\end{ | \end{array} \right] | ||
\begin{ | \left[ \begin{array} {rrr} | ||
1 & -2 \\ | 1 & -2 \\ | ||
0 & 0 \\ | 0 & 0 \\ | ||
0 & 1 \\ | 0 & 1 \\ | ||
\end{ | \end{array} \right] = | ||
\begin{ | \left[ \begin{array} {rrr} | ||
1 & -2 \\ | 1 & -2 \\ | ||
0 & 4 \\ | 0 & 4 \\ | ||
\end{ | \end{array} \right] | ||
</math> | </math> | ||
| Line 139: | Line 139: | ||
<math> | <math> | ||
\begin{ | \left[ \begin{array} {rrr} | ||
1 & \frac12 \\ | 1 & \frac12 \\ | ||
0 & \frac14 \\ | 0 & \frac14 \\ | ||
\end{ | \end{array} \right] | ||
</math> | </math> | ||
| Line 148: | Line 148: | ||
<math> | <math> | ||
\begin{ | \left[ \begin{array} {rrr} | ||
1 & -2 \\ | 1 & -2 \\ | ||
0 & 0 \\ | 0 & 0 \\ | ||
0 & 1 \\ | 0 & 1 \\ | ||
\end{ | \end{array} \right] | ||
\begin{ | \left[ \begin{array} {rrr} | ||
1 & \frac12 \\ | 1 & \frac12 \\ | ||
0 & \frac14 \\ | 0 & \frac14 \\ | ||
\end{ | \end{array} \right] = | ||
\begin{ | \left[ \begin{array} {rrr} | ||
1 & 0 \\ | 1 & 0 \\ | ||
0 & 0 \\ | 0 & 0 \\ | ||
0 & \frac14 \\ | 0 & \frac14 \\ | ||
\end{ | \end{array} \right] | ||
</math> | </math> | ||
| Line 169: | Line 169: | ||
<math> | <math> | ||
\begin{ | \left[ \begin{array} {rrr} | ||
1 & 1 \\ | 1 & 1 \\ | ||
0 & 1 \\ | 0 & 1 \\ | ||
0 & -1 \\ | 0 & -1 \\ | ||
\end{ | \end{array} \right] | ||
</math> | </math> | ||
| Line 179: | Line 179: | ||
<math> | <math> | ||
\begin{ | \left[ \begin{array} {rrr} | ||
1 & 0 & -4 \\ | 1 & 0 & -4 \\ | ||
0 & 1 & 4 \\ | 0 & 1 & 4 \\ | ||
\end{ | \end{array} \right] | ||
\begin{ | \left[ \begin{array} {rrr} | ||
1 & 1 \\ | 1 & 1 \\ | ||
0 & 1 \\ | 0 & 1 \\ | ||
0 & -1 \\ | 0 & -1 \\ | ||
\end{ | \end{array} \right] = | ||
\begin{ | \left[ \begin{array} {rrr} | ||
1 & 2 \\ | 1 & 2 \\ | ||
0 & -3 \\ | 0 & -3 \\ | ||
\end{ | \end{array} \right] | ||
</math> | </math> | ||
| Line 197: | Line 197: | ||
<math> | <math> | ||
\begin{ | \left[ \begin{array} {rrr} | ||
1 & \frac23 \\ | 1 & \frac23 \\ | ||
0 & -\frac13 \\ | 0 & -\frac13 \\ | ||
\end{ | \end{array} \right] | ||
</math> | </math> | ||
| Line 206: | Line 206: | ||
<math> | <math> | ||
\begin{ | \left[ \begin{array} {rrr} | ||
1 & 1 \\ | 1 & 1 \\ | ||
0 & 1 \\ | 0 & 1 \\ | ||
0 & -1 \\ | 0 & -1 \\ | ||
\end{ | \end{array} \right] | ||
\begin{ | \left[ \begin{array} {rrr} | ||
1 & \frac23 \\ | 1 & \frac23 \\ | ||
0 & -\frac13 \\ | 0 & -\frac13 \\ | ||
\end{ | \end{array} \right] = | ||
\begin{ | \left[ \begin{array} {rrr} | ||
1 & \frac13 \\ | 1 & \frac13 \\ | ||
0 & -\frac13 \\ | 0 & -\frac13 \\ | ||
0 & \frac13 \\ | 0 & \frac13 \\ | ||
\end{ | \end{array} \right] | ||
</math> | </math> | ||