> \prod_{i=1}^k H(v_i)

[xjzhao001]

\prod_{i=1}^k H(v_i), is that right?
Right.
Hi, toshas, your work is great, thanks!
You confirm that if we denote H(v) = I_n - v v^T / \norm{v}^2 a Householder reflection, the torch_householder_orgqr() computes \prod_{i=1}^k H(v_i), and I have two questions, one is I think H(v) = I_n – 2vv^T/\norm{v}^2, and the other is \prod_{i=1}^k H(v_i) means H_1* H_2*…H_(n-1) or H_(n-1)* H_(n-2)…H_1 ? If it is H_1 H_2*…H_(n-1), it refers to Q in QR decomposition, right? But you said earlier that this is not a QR decomposition, so I feel a little confused. Hope to get your prompt reply, thank you.

[toshas]

H(v) = I_n - 2 v v^T / \norm{v}^2 is the correct equation.
For the rest of your questions, please refer to our paper which explains this aspect in a greater detail: https://arxiv.org/pdf/2103.04217.pdf