3 ms·
Most people do not learn this version. This algorithm produces a bunch of intermediate matrices of (n-1)x(n-1) size, (n-2)x(n-2), etc. (See https://en.wikipedi
by ajkjk 3y ago
Most people do not learn this version.
This algorithm produces a bunch of intermediate matrices of (n-1)x(n-1) size, (n-2)x(n-2), etc. (See https://en.wikipedia.org/wiki/Dodgson_condensation https://en.wikipedia.org/wiki/Dodgson_condensation also, which is honestly more useful than this article.)
The usual manual algorithm is something like "go along the top row, and for each value multiply it by the determinant of the minor created by removing that row and column, times an alternating sign". It involves smaller determinants but never produces a 'smaller intermediate matrix'. It's also, as far as I can tell, a lot less work than the Dodgson method.
- FooBarBizBazz 3y ago> The usual manual algorithm is something like "go along the top row, and for each value multiply it by the determinant of the minor created by removing that row and column, times an alternating sign". Cofactor expansion, aka Laplace expansion. ("Cofactor" is probably a better name, since everything else is also named after Laplace, or Gauss, or Euler.) > It's also, as far as I can tell, a lot less work than the Dodgson method. That's the interesting thing. It isn't! The article discusses the asymptotics at the end.
- ajkjk 3y agooh yeah, the name escaped me earlier but, of course, it is cofactor expansion.