### HW 4 - ex2

Hello,
I am having a lot of trouble trying to understand how the matrix A, in the solutions to parts a) and b), is determined ...
In a) it seems we have a 1 in aij if user i has rated item j but for part b) I am confused.

Thank you

Top comment

To write the minimization problem in the standard form, we need to collect all of the parameters over which we optimize into the vector $$b$$, so in (b), $$b$$ is the concatenation of all the user biases $$b_u$$ followed by the item biases $$b_i$$. Then each row of $$A$$ captures one term $$r_{ui}-\bar{r}- b_u - b_i$$, so has two ones, one at position $$u$$, and one at position $$n+i$$.

I hope this clarifies it?

I think the problem lies in the fact that the solution places the second one at position u + i and not n + i. Is this a typo ?

Yes indeed, it's yet another typo - sorry, I didn't even catch it after writing the explanation above.

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