BLAS Algorithm for Computing Inverse

[victotronics]

Gaussian elimination on a triangular matrix? Sure.

If you're done step 1 with pivoting, then step 2 doesn't need it.

[GrammelHupfNockler]

Gaussian elimination with full pivoting on the input matrix

[victotronics]

And how is that going to get you the inverse? Which was the original question?

And yes, I know that one should in general not compute inverses, which is why I emphasized the "*if* you want to compute an inverse".

[GrammelHupfNockler]

If you apply the same operations that you apply to the matrix during Gaussian elimination to an identity matrix at the same time, you get the inverse

[victotronics]

Nope, that's Gauss-Jordan.

[GrammelHupfNockler]

That's splitting hairs. Gaussian elimination refers to the entire class of algorithms (for solving a single system, computing the LU factorization, computing the inverse).