On: Seven sins of numerical linear algebra

[gwgundersen]

Re: the first sin, I was told to not invert matrices but never given a satisfying reason. So I wrote a blog post about it:

http://gregorygundersen.com/blog/2020/12/09/matrix-inversion...

[Mathnerd314 → gwgundersen]

The other obvious reason to avoid inverses is that they're only defined for square matrices, whereas LU decomposition works on general rectangular matrices (or rather PLU decomposition,same basic idea).

[bee_rider → gwgundersen]

Invert can also destroy structure you might want to keep around, for example the LU factorization of a banded matrix will still be banded (lapack will do partial pivoting which will increase the bandwidth, but with it'll only double the number of super-diagonals in L), while the inverse is a full matrix.

[bee_rider → bee_rider]

Err, the number of super-diagonals in U obviously, haha, oops.