Instructional Video7:12
Professor Dave Explains

Solving Systems Using Cramer's Rule

12th - Higher Ed
How to solve systems of linear equations using Cramer's rule.
Instructional Video16:39
Professor Dave Explains

Finding Eigenvalues and Eigenvectors

12th - Higher Ed
Defining eigenvalues and eigenvectors, and outlining how to solve for them given a particular matrix.
Instructional Video8:40
Professor Dave Explains

Linear Transformations on Vector Spaces

12th - Higher Ed
How to perform linear transformations on vector spaces.
Instructional Video8:10
Professor Dave Explains

Understanding Vector Spaces

12th - Higher Ed
An introduction to vector spaces.
Instructional Video14:05
Looking Glass Universe

Matrices make sense: Linear transformations and matrix multiplication

12th - Higher Ed
Matrices are often presented as a useful bookkeeping/ commutation tools to students- but there's much more to them. When you understand what a Matrix really is so many parts of Linear Algebra will be completely obvious to you, including...
Instructional Video9:35
Professor Dave Explains

Basis and Dimension

12th - Higher Ed
Defining basis and dimension.
Instructional Video17:30
Looking Glass Universe

Matrix inverses make sense - A simple condition for when the inverse exists

12th - Higher Ed
This video is about matrix inverses, and in particular, I try to give a bit more intuition for them- rather than just giving you the formula for the determinant, Cramner's rule, the inverse of 2x2 and 3x3 matrices etc. Along the way, we...
Instructional Video8:29
Professor Dave Explains

Complex, Hermitian, and Unitary Matrices

12th - Higher Ed
Defining complex matrices, hermitian matrices, and unitary matrices.
Instructional Video10:13
Professor Dave Explains

Introduction to Linear Algebra: Systems of Linear Equations

12th - Higher Ed
An introduction to linear algebra.
Instructional Video10:32
Zach Star

How Much Math do Engineers Use? (College Vs Career)

12th - Higher Ed
In this video I discuss "How much math do engineers use?" Specifically I dive into the math they use in college vs their career. For a video like this there isn't a right answer because there are millions of engineers out there all with...
Instructional Video4:33
Fun Robotics

NumPy Library Part 1

Higher Ed
Investigating the NumPy Python library and how to use it efficiently
Instructional Video13:43
Looking Glass Universe

Vectors make sense - Vector addition and basis vectors

12th - Higher Ed
Vectors may seem very difficult when youre first introduced to them, but I hope this video helps you see theyre not that scary! This is the start of a whole series of linear algebra, and I will cover vectors, the scalar product,...
Instructional Video9:59
1
1
3Blue1Brown

Linear Combinations, Span, and Basis Vectors | Essence of Linear Algebra, Chapter 2

11th - Higher Ed Standards
What does it mean for two vectors to be linearly independent? The resource presents the basics of basis vectors and linear combinations. The third video in the 15-part series provides a definition of linear independence in terms of the...
Instructional Video11:06
Domain of Science

The Map of Mathematics

9th - Higher Ed
How does all this math fit together? The resource creates a graphical view of the extent of mathematics. The map shows the pure and applied sides of studying mathematics and breaks them down into their many disciplines.
Instructional Video16:46
1
1
3Blue1Brown

Abstract Vector Spaces | Essence of Linear Algebra, Chapter 11

11th - Higher Ed
Take the principles of vectors and apply them to other things that act like vectors. The last video in the series of 15 introduces the more abstract aspects of linear algebra, making the connection back to the vector concepts discussed...
Instructional Video17:16
1
1
3Blue1Brown

Eigenvectors and Eigenvalues | Essence of Linear Algebra, Chapter 10

11th - Higher Ed Standards
Find vectors that stay on their spans after a linear transformation. The 14th video in the series of 15 introduces the concept of eigenvectors, vectors that are only scaled during a linear transformation. The presentation illustrates the...
Instructional Video12:51
1
1
3Blue1Brown

Change of Basis | Essence of Linear Algebra, Chapter 9

11th - Higher Ed Standards
It is all about perspective. A video introduces the idea that the view of a vector all depends upon the perspective of the basis vectors. Knowing how to go from one coordinate system's basis vectors to another system's basis vectors...
Instructional Video13:10
1
1
3Blue1Brown

Cross Products in the Light of Linear Transformations | Essence of Linear Algebra Chapter 8 Part 2

11th - Higher Ed Standards
What do cross products and parallelpipeds have in common? The video discusses the geometric representation of the cross product. The geometric interpretation explains why the computational trick in calculating the cross product works.
Instructional Video9:52
1
1
3Blue1Brown

Vectors, What Even Are They? | Essence of Linear Algebra, Chapter 1

11th - Higher Ed Standards
Take a look at vectors as geometric objects and then as an algebraic concept. The second video in a series of 15 introduces the vector using three perspectives: the physics, computer science, and mathematical. The resource shows the...
Instructional Video8:54
1
1
3Blue1Brown

Cross Products | Essence of Linear Algebra, Chapter 8

11th - Higher Ed
Equate the area of a parallelogram with the magnitude. The 11th installment in a 15-video series introduces the concept of the cross product of two vectors. The presentation makes the geometric connection between the cross product, the...
Instructional Video14:12
1
1
3Blue1Brown

Dot Products and Duality | Essence of Linear Algebra, Chapter 7

11th - Higher Ed Standards
The dot product of two matrices is a number on the number line, its transformation. The resource presents the dot product as a linear transformation from two dimensions to one dimension. The video uses the numerical and graphical...
Instructional Video4:27
1
1
3Blue1Brown

Nonsquare Matrices as Transformations Between Dimensions | Essence of Linear Algebra, Footnote

11th - Higher Ed Standards
But what happens if the matrix is not square? The ninth video in a series of 15 serves as a footnote to discuss non-square matrices. The resource presents them as transformations between two and three dimensions. The presentation...
Instructional Video12:09
1
1
3Blue1Brown

Inverse Matrices, Column Space and Null Space | Essence of Linear Algebra, Chapter 6

11th - Higher Ed Standards
Determine the geometric representation to the solution of a system of linear equations. The resource shows how scholars can represent a system of linear equations as a linear transformation. The video discusses using an inverse...
Instructional Video10:03
1
1
3Blue1Brown

The Determinant | Essence of Linear Algebra, Chapter 5

11th - Higher Ed Standards
Determine how much a linear transformation alters area. The seventh segment in a series of 15 makes the connection between the determinant and the scale factor of areas during a linear transformation. The video goes on to explain the...