Linear combinations, span, and basis vectors | Essence of linear algebra, chapter 2

Linear combinations, span, and basis vectors | Essence of linear algebra, chapter 2

In the last video, along with the ideas of vector addition and scalar multiplication, I described vector coordinates, where’s this back and forth between, for example, pairs of numbers and two-dimensional vectors. Now, I imagine that vector coordinates were already familiar to a lot of you, but there’s another kind of interesting way to think

The determinant | Essence of linear algebra, chapter 6

The determinant | Essence of linear algebra, chapter 6

Hello, hello again. So, moving forward I will be assuming you have a visual understanding of linear transformations and how they’re represented with matrices the way I have been talking about in the last few videos. If you think about a couple of these linear transformations you might notice how some of them seem to

How to paint shiny 3D cherries in watercolor

How to paint shiny 3D cherries in watercolor

Hi it’s Anna Mason and in this watercolour tip video I wanted so show you how I went about painting These shiny, juicy cherries. Specifically I wanted to focus in and show you how to create the transitions between the highlights and the dark skin of the cherry around them. Because getting this right really

Dot products and duality | Essence of linear algebra, chapter 9

Dot products and duality | Essence of linear algebra, chapter 9

Traditionally, dot products or something that’s introduced really early on in a linear algebra course typically right at the start. So it might seem strange that I push them back this far in the series. I did this because there’s a standard way to introduce the topic which requires nothing more than a basic understanding

Matrix multiplication as composition | Essence of linear algebra, chapter 4

Matrix multiplication as composition | Essence of linear algebra, chapter 4

It is my experience that proofs involving matrices can be shortened by 50% if one throws matrices out. — Emil Artin Hey everyone! Where we last left off, I showed what linear transformations look like and how to represent them using matrices. This is worth a quick recap, because it’s just really important. But of

Gradient descent, how neural networks learn | Deep learning, chapter 2

Gradient descent, how neural networks learn | Deep learning, chapter 2

Last video I laid out the structure of a neural network I’ll give a quick recap here just so that it’s fresh in our minds And then I have two main goals for this video. The first is to introduce the idea of gradient descent, which underlies not only how neural networks learn, but how

Cross products | Essence of linear algebra, Chapter 10

Cross products | Essence of linear algebra, Chapter 10

Last video, I’ve talked about the dot product. Showing both the standard introduction to the topic, as well as a deeper view of how it relates to linear transformations. I’d like to do the same thing for cross products, which also have a standard introduction along with a deeper understanding in the light of linear

What they won’t teach you in calculus

What they won’t teach you in calculus

3Blue1Brown [Classical music] Picture yourself as an early calculus student about to begin your first course: The months ahead of you hold within them a lot of hard work Some neat examples, some not so neat examples, beautiful connections to physics, not so beautiful piles of formulas to memorise, plenty of moments of getting stuck

K-Means Clustering Visualization – Intro to Machine Learning

K-Means Clustering Visualization – Intro to Machine Learning

And I hope you said three, it’s pretty obvious that there should be three centroids here. So let’s add three, one, two, three. So they’re all starting out right next to each other, but we’ll see how as the algorithm progresses, they end up in the right place.

Higher order derivatives | Essence of calculus, chapter 10

In the next chapter, about Taylor series, I make frequent reference to higher order derivatives. And, if you’re already comfortable with second derivatives, third derivatives and such, great! Feel free to skip right ahead to the main event now, you won’t hurt my feelings. But somehow I’ve managed not to bring up higher order derivatives