Tag Archives: blue

The hardest problem on the hardest test

Do you guys know about the Putnam? It’s a math competition for undergraduate students. It’s 6 hours long and consists of 12 questions, broken up into two different 3-hour sessions. With each question being scored on a 1-10 scale, the highest possible score is 120. And yet, despite the fact that the only students taking… Read More »

Rooster Teeth Animated Adventures – Gavin or Google #1: Breaking Babies

Burnie: (singing) Gavin or Google, Google or Gavin, Which one said it? Let’s find out, hey! Gavin: I’m feelin’ lucky! Burnie: The first phrase that I gave to both Gavin and Google is… “Can you break…” Burnie: First return… (Barbara laughs) “Can you break your own neck if you really wanted to?” The other’s return:… Read More »

Eigenvectors and eigenvalues | Essence of linear algebra, chapter 14

“Eigenvectors and eigenvalues” is one of those topics that a lot of students find particularly unintuitive. Questions like “why are we doing this” and “what does this actually mean” are too often left just floating away in an unanswered sea of computations. And as I put out the videos of the series, a lot of… Read More »

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… Read More »

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… Read More »

Nonsquare matrices as transformations between dimensions | Essence of linear algebra, chapter 8

Hey, everyone! I’ve got another quick footnote for you between chapters today. When I talked about linear transformation so far, I’ve only really talked about transformations from 2-D vectors to other 2-D vectors, represented with 2-by-2 matrices; or from 3-D vectors to other 3-D vectors, represented with 3-by-3 matrices. But several commenters have asked about… Read More »

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

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,… Read More »

Change of basis | Essence of linear algebra, chapter 13

If I have a vector sitting here in 2D space we have a standard way to describe it with coordinates. In this case, the vector has coordinates [3, 2], which means going from its tail to its tip involves moving 3 units to the right and 2 units up. Now, the more linear-algebra-oriented way to… Read More »

Introducing Gmail Blue

Gmail Blue was part of the initial conception for Gmail when it was launched. At the time the technology was simply not there. The culture of Google really is to incorporate Moonshot thinking into every project. It’s taken us six years to develop the technology to achieve Gmail Blue. Our major challenge was how do… Read More »

Inverse matrices, column space and null space | Essence of linear algebra, chapter 7

As you can probably tell by now, the bulk of this series is on understanding matrix and vector operations through that more visual lens of linear transformations. This video is no exception, describing the concepts of inverse matrices, column space, rank, and null space through that lens. A forewarning though: I’m not going to talk… Read More »