6 ms·

Not trying to cheapen anything about this article, but I'm very sure this is how I was taught to calculate them in several schools. Have any of you been taught

Not trying to cheapen anything about this article, but I'm very sure this is how I was taught to calculate them in several schools. Have any of you been taught otherwise?

nwoli 3y ago
> Charles Dodgson, better known by his pen name Lewis Carroll, discovered a method of calculating determinants now known variously as the method of contractants Emphasis on discovered
- hgsgm 3y ago
  It's linear algebra. There are many slightly different ways to do any computation in linear algebra. (This is the essence of the fuss among mathphobes about Common Core, when people complain about kids learning different algorithms for arithmetic.)
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 ago
    oh yeah, the name escaped me earlier but, of course, it is cofactor expansion.

Not trying to cheapen anything about this article, but I'm very sure this is how I was taught to calculate them in several schools. Have any of you been taught otherwise?

nwoli 3y ago

> Charles Dodgson, better known by his pen name Lewis Carroll, discovered a method of calculating determinants now known variously as the method of contractants Emphasis on discovered

hgsgm 3y ago
It's linear algebra. There are many slightly different ways to do any computation in linear algebra. (This is the essence of the fuss among mathphobes about Common Core, when people complain about kids learning different algorithms for arithmetic.)

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 ago
  oh yeah, the name escaped me earlier but, of course, it is cofactor expansion.