The standard matrix multiplication together with its inverse is sort of solely what’s occurring in lots of easy ML fashions

That is the fourth chapter of the in-progress ebook on linear algebra, “A birds eye view of linear algebra”. The desk of contents to this point:

1. Chapter-1: The fundamentals
2. Chapter-2: The measure of a map — determinants
3. Chapter-3: Why is matrix multiplication the way in which it’s?
4. Chapter-4 (present): Techniques of equations, linear regression and neural networks

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Fashionable AI fashions leverage excessive dimensional vector areas to encode info. And the software we’ve for reasoning about excessive dimensional areas and mappings between them is linear algebra.

And inside that area, matrix multiplication (together with its inverse) is actually all you should construct many easy machine studying fashions finish to finish. Which is why spending the time to know it very well is a good funding. And that is what we did in chapter 3.

These easy fashions, helpful in their very own proper, type the constructing blocks of extra advanced ML and AI fashions with state-of-the-art efficiency.

We’ll cowl a couple of of those functions (from linear regression to elementary neural networks) on this chapter.

However first, we have to go to the best case within the easiest mannequin — when the variety of information factors equals the variety of mannequin parameters. The case of fixing a system of linear equations.

Now we have lastly arrived (within the context of this ebook) on the coronary heart of linear algebra. Fixing techniques of linear equations is how we found linear algebra within the first place and the motivations for many ideas on this area have deep roots on this utility.

Let’s begin easy and one dimensional. The idea of division is rooted in a single…