I saw this insightful discussion on Slack (Made some editing for clarity):

The

`\`

(Operator) should produce the minimum norm solution if many exist, and that’s what it does.

I am not sure

`\`

will always yield the minimum norm vector. At least it doesn’t on MATLAB. Which uses`QR`

for basic solution for non square matrices.

@ Andreas Noack:

[In Julia]

`/`

will give a minimum norm solution for rectangular problems but not square problems (which is indeed a bit odd).

When the problem is underdetermined, MATLAB produces a basic solution (i.e. with zeros) whereas Julia chooses the minimum norm solution. The latter but not the former is built into some LAPACK routines. However, it’s quite easy to build a basic solution from a pivoted QR.

@ Dominique:

Also,

`\`

only returns the min-norm solution if A is dense. If A is sparse (and rectangular),`\`

returns abasicsolution, i.e., one with many zeros.

If anyone else had more info to add, please do.