So we're gonna talk about least squares. It's something you've probably seen in a couple of different contexts, and it concerns overdetermined linear equations. So we have a set of over determined linear equations. Now, here we have y=ax, where a is we'll make strictly skinny. It's overdetermined because you have more equations than unknowns. And, of course, unless y is in the range of a, which if you pick y randomly, and rm is an event of probability zero, you can't solve y=ax. So one method to approximately solve y=ax, and it's very important to emphasize here we're not actually solving y=ax, is to choose x to minimize the norm of this residual. ...

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