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Linear transformations and matrices | Essence of linear algebra, chapter 3

October 13, 2019 at 5:29 pm | Articles, Blog | Ruben Talley -

Unfortunately, no one can be told, what the Matrix is. You have to see it for yourself. – Morpheus Surprisingly apt words on the importance of understanding matrix operations visually Hey everyone! If I had to choose just one topic that makes all of the others in linear algebra start to click and which too

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“Linear transformations and matrices | Essence of linear algebra, chapter 3”

Solving 2D equations using color, a story of winding numbers and composition

September 17, 2019 at 5:29 pm | Articles, Blog | Ruben Talley -

There’s two things here, the main topic, and the meta topic. The main topic is a neat algorithm for solving many two-dimensional equations. That is, equations with two unknown real numbers, or perhaps those involving a single unknown which is a complex number. So for example, if you want to find the complex roots of

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“Solving 2D equations using color, a story of winding numbers and composition”

What is backpropagation really doing? | Deep learning, chapter 3

September 4, 2019 at 4:29 pm | Articles, Blog | Ruben Talley -

Here we tackle backpropagation, the core algorithm behind how neural networks learn. After a quick recap for where we are, the first thing I’ll do is an intuitive walkthrough for what the algorithm is actually doing without any reference to the formulas, Then for those of you who do want to dive into the math,

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“What is backpropagation really doing? | Deep learning, chapter 3”

Cross products in the light of linear transformations | Essence of linear algebra chapter 11

September 2, 2019 at 4:29 pm | Articles, Blog | Ruben Talley -

Hey folks! Where we left off, I was talking about how to compute a three-dimensional cross product between two vectors, v x w. It’s this funny thing where you write a matrix, whose second column has the coordinates of v, whose third column has the coordinates of w, but the entries of that first column,

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“Cross products in the light of linear transformations | Essence of linear algebra chapter 11”

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

August 25, 2019 at 1:29 pm | Articles, Blog | Ruben Talley -

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

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