3 ms·

So grateful something mentioned this man. Strang is just amazing. When I first moved to Cambridge, his corresponding book was a relatively expensive prospect, a

So grateful something mentioned this man. Strang is just amazing. When I first moved to Cambridge, his corresponding book was a relatively expensive prospect, and I was rather serious about 18.06, so ascertaining its book was very important to me. He was gracious enough to gift me a copy that I still have and cherish to this day. Some real moments of thrilling discovery happened for me, it was exhilarating, though trite as they may be! Like in implementing a program for general inversion of any MxN matrix, one would typically perform the Gaussian elimination (going down) and then the Jordan (going back up) and finally divide by the scalars in the pivot columns. But, as it turns out, it's a much simpler program if you do Gauss elimination, literally rotate all matrices by 180 degrees, do Gauss elimination again, then rotate everything back, and then address the non-unit pivot columns. src: https://github.com/wittedhaddock/AlgebraicCircumscriptions/blob/master/AlgebraicCircumscriptions/ACMatrix.swift#L138 https://github.com/wittedhaddock/AlgebraicCircumscriptions/b...

dxbydt 7y ago
> general inversion of any MxN matrix ??! is there such a thing ? only nonsingular square matrices can be inverted. a general mxn matrix may have a “left inverse” or a “right inverse”, but i don’t think your code is computing that.
- deleted 7y ago
  [deleted]
- throw20102010 7y ago
  There is such a thing as a generalized inverse, in which you can invert non-square or non-full rank matrices and the generalized inverse meets many (but not all) of the properties of an inverse. The tough part is that the agreed upon set of properties does not create a unique solution for a generalized inverse like it does for the inverse, so there are multiple possibilities when someone says generalized inverse. However, the most popular is probably the Moore-Penrose inverse: https://en.wikipedia.org/wiki/Moore–Penrose_inverse https://en.wikipedia.org/wiki/Moore–Penrose_inverse
  - wittedhaddock 7y ago
    thank you very much for this !!
- wittedhaddock 7y ago
  You're 100% correct, the algo only handles square matrices! Typo. So, disclaimer, where m === n :) thanks!

dxbydt 7y ago

> general inversion of any MxN matrix ??! is there such a thing ? only nonsingular square matrices can be inverted. a general mxn matrix may have a “left inverse” or a “right inverse”, but i don’t think your code is computing that.

deleted 7y ago
[deleted]
throw20102010 7y ago
There is such a thing as a generalized inverse, in which you can invert non-square or non-full rank matrices and the generalized inverse meets many (but not all) of the properties of an inverse. The tough part is that the agreed upon set of properties does not create a unique solution for a generalized inverse like it does for the inverse, so there are multiple possibilities when someone says generalized inverse. However, the most popular is probably the Moore-Penrose inverse: https://en.wikipedia.org/wiki/Moore–Penrose_inverse https://en.wikipedia.org/wiki/Moore–Penrose_inverse
- wittedhaddock 7y ago
  thank you very much for this !!
wittedhaddock 7y ago
You're 100% correct, the algo only handles square matrices! Typo. So, disclaimer, where m === n :) thanks!