A correction

Hi all,

Towards the end of today's lecture we discussed counting FLOPs and I said that matrix multiplication requires O(n^2) FLOPs. That's of course wrong -- apologies for the confusion! What I had in mind was matrix-vector multiplication, because we had previously talked about solving matrix equations by doing matrix-vector multiplication with an inverse matrix. But if we are talking about matrix-matrix multiplication, that requires O(n^3) FLOPs, when using the naive method.

I have extended the chapter on counting FLOPs in the lecture notes with examples that explain matrix-vector and matrix-matrix multiplication, so have a look there if you want to see the details.

But, there exists faster algorithms for matrix multiplication, and this is a live field of research -- see e.g. these news stories:

• https://www.quantamagazine.org/mathematicians-inch-closer-to-matrix-multiplication-goal-20210323/
• https://www.quantamagazine.org/new-breakthrough-brings-matrix-multiplication-closer-to-ideal-20240307/

Best,
Anders