August 6, 2016
Kicking off the linear algebra lessons, let's make sure we're all on the same page about how specifically to think about vectors in this context.
August 7, 2016
The fundamental vector concepts of span, linear combinations, linear dependence, and bases all center on one surprisingly importan...Read more
August 7, 2016
Matrices can be thought of as transforming space, and understanding how this work is crucial for understanding many other ideas th...Read more
August 9, 2016
Multiplying two matrices represents applying one transformation after another. Many facts about matrix multiplication become much...Read more
August 10, 2016
What do 3d linear transformations look like? Having talked about the relationship between matrices and transformations in the las...Read more
August 11, 2016
The determinant of a linear transformation measures how much areas/volumes change during the transformation.
August 16, 2016
How to think about linear systems of equations geometrically. The focus here is on gaining an intuition for the concepts of inver...Read more
August 16, 2016
Because people asked, this is a video briefly showing the geometric interpretation of non-square matrices as linear transformation...Read more
August 24, 2016
Dot products are a nice geometric tool for understanding projection. But now that we know about linear transformations, we can ge...Read more
September 1, 2016
This covers the main geometric intuition behind the 2d and 3d cross products.
September 3, 2016
For anyone who wants to understand the cross product more deeply, this video shows how it relates to a certain linear transformati...Read more
March 17, 2019
This rule seems random to many students, but it has a beautiful reason for being true.
September 11, 2016
How do you translate back and forth between coordinate systems that use different basis vectors?
September 15, 2016
A visual understanding of eigenvectors, eigenvalues, and the usefulness of an eigenbasis.
May 7, 2021 • 13m
How to write the eigenvalues of a 2x2 matrix just by looking at it.
September 24, 2016 • 17m
This is really the reason linear algebra is so powerful.