Linear Algebra

Topics

Core concepts in linear algebra with applications to Machine Learning.

Notes

Systems of Equations

linear-algebra

The first topic you learn in linear algebra is systems of linear equations. However, before you delve into equations, it is important to understand the language of…

Solving Systems of Linear Equations: Elimination

linear-algebra

You are now ready to learn something that has been lurking yet present in the previous lessons. In one of the first quizzes, you took a system of linear equations and found…

Solving Systems of Linear Equations: Row Echelon Form and Rank

linear-algebra

Throughout the last few sections, there has been a concept that you’ve seen yet still have not been formally introduced to. It is the notion of the rank of a matrix which in…

Gaussian Elimination Algorithm

linear-algebra

Now you’re ready to learn a very famous and classic algorithm called Gaussian elimination. You will see that this is just the elimination method you studied before, but…

Vector Algebra

linear-algebra

So far you’ve been working with systems of equations and matrices, solving them by elimination, reducing them to row echelon form, and running Gaussian elimination. Now it’s…

Linear Transformations

linear-algebra

In the previous notes you have seen matrices as arrays of numbers that represent systems of linear equations. But there is another very powerful and very useful way to think…

Determinants In-depth

linear-algebra

The determinant is a scalar value computed from a square matrix \(A \in \mathbb{R}^{n \times n}\), denoted \(\det(A)\) or \(|A|\).

Eigenvalues and Eigenvectors

linear-algebra

For a square matrix \(A \in \mathbb{R}^{n \times n}\), a scalar \(\lambda\) is an eigenvalue and non-zero vector \(\mathbf{v}\) is its corresponding eigenvector if: