linear algebra week1 vectors

So the first thing we need to doin this course on Linear Algebra is to get a handle on vectors, which will turn out to be really useful for us in solving those linear algebra problems.

Now actually, if we could find what the steepest way down the hill was, then we could go down this set of contours, this sort of landscape here towards the minimum point, towards the point where get the best possible fit.

And what we're doing here, these are vectors, these are little moves around space. They're not moves around a physical space, they're moves around a parameter space, but it's the same thing.

And write those all down in a list that was a vector. (different attributes)

When we put it like that, it's not so crazy to think of the space of all the fitting parameters of a function, and then of vectors as being things that take us around that space.

So to do this well, we'll want to understand how to work with vectors and then how to do calculus on those vectors in order to find gradients in these contour maps and minima and all those sorts of things.

Moves around these fitting parameter space are then just vectors in that space of fitting parameters.