Professor Dave Explains
Solving Systems Using Cramer's Rule
How to solve systems of linear equations using Cramer's rule.
Professor Dave Explains
Finding Eigenvalues and Eigenvectors
Defining eigenvalues and eigenvectors, and outlining how to solve for them given a particular matrix.
Professor Dave Explains
Linear Transformations on Vector Spaces
How to perform linear transformations on vector spaces.
Looking Glass Universe
Matrices make sense: Linear transformations and matrix multiplication
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...
Looking Glass Universe
Matrix inverses make sense - A simple condition for when the inverse exists
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...
Professor Dave Explains
Complex, Hermitian, and Unitary Matrices
Defining complex matrices, hermitian matrices, and unitary matrices.
Professor Dave Explains
Introduction to Linear Algebra: Systems of Linear Equations
An introduction to linear algebra.
Zach Star
How Much Math do Engineers Use? (College Vs Career)
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...
Fun Robotics
NumPy Library Part 1
Investigating the NumPy Python library and how to use it efficiently
Looking Glass Universe
Vectors make sense - Vector addition and basis vectors
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,...
3Blue1Brown
Linear Combinations, Span, and Basis Vectors | Essence of Linear Algebra, Chapter 2
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...
Domain of Science
The Map of Mathematics
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.
3Blue1Brown
Abstract Vector Spaces | Essence of Linear Algebra, Chapter 11
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...
3Blue1Brown
Eigenvectors and Eigenvalues | Essence of Linear Algebra, Chapter 10
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...
3Blue1Brown
Change of Basis | Essence of Linear Algebra, Chapter 9
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...
3Blue1Brown
Cross Products in the Light of Linear Transformations | Essence of Linear Algebra Chapter 8 Part 2
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.
3Blue1Brown
Vectors, What Even Are They? | Essence of Linear Algebra, Chapter 1
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...
3Blue1Brown
Cross Products | Essence of Linear Algebra, Chapter 8
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...
3Blue1Brown
Dot Products and Duality | Essence of Linear Algebra, Chapter 7
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...
3Blue1Brown
Nonsquare Matrices as Transformations Between Dimensions | Essence of Linear Algebra, Footnote
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...
3Blue1Brown
Inverse Matrices, Column Space and Null Space | Essence of Linear Algebra, Chapter 6
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...
3Blue1Brown
The Determinant | Essence of Linear Algebra, Chapter 5
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...