Defactoring: Difference between revisions
Cmloegcmluin (talk | contribs) |
Cmloegcmluin (talk | contribs) |
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\end{array} \right]</math> | \end{array} \right]</math> | ||
And now we're going to augment it to the right, so we can do the first step of the Hermite decomposition. But we're actually going to go a bit further. We're going to go ahead and augment it to the right and also augment the augmenting matrix to the bottom, because that's where we're going to perform the next step, which is the inversion. We learned inversion using augmentation to the right, but remember: everything we're doing here is transposed! So augmenting to the bottom is the correct thing to do there. When we're all done, we'll transpose one more time to undo it. | And now we're going to augment it to the right, so we can do the first step of the Hermite decomposition. But we're actually going to go a bit further. We're going to go ahead and augment it to the right and also augment the augmenting matrix to the bottom, because that's where we're going to perform the next step, which is the inversion. We learned inversion using augmentation to the right, but remember: everything we're doing here is transposed! So augmenting to the bottom is the correct thing to do there. When we're all done, we'll transpose one more time to undo it. (In the Wolfram Language code it was more natural to transpose things between the Hermite decomposition and the inversion, but here I think the process is better illustrated with this rotated-L-shape structure.) | ||
<math> \begin{array} {l} \begin{array} {l} \left[ \begin{array} {rrr} | <math> \begin{array} {l} \begin{array} {l} \left[ \begin{array} {rrr} |