Julia Linear Algebra Tutorials

This repository is a work in progress.

This repository contains tutorials that go alongside the textbook Introduction to Linear Algebra by Gilbert Strang. [1] Additional materials may be included in these tutorials not found in the textbook. Where they occur, they will be properly cited and referenced in that corresponding notebook. Please read the Set-up Requirements before working on the tutorials. The tutorials will not work if one does not follow the set-up.

Set-up Requirements

NOTE: This has been tested on Julia 1.4.1.

Cloning Project

Each tutorial is contained in a Jupyter notebook. To set-up this tutorial repository, clone the repository:

git clone https://github.com/TheCedarPrince/LinAlgTuts.jl

Running the Notebooks

Then, navigate inside the cloned directory and execute the following in your Julia REPL:

julia> using Pkg

julia> Pkg.activate()

Once this has been activated, you can open the server to view the Jupyter notebooks as shown below:

julia> using IJulia

julia> jupyterlab()

Or, if you want the classic Jupyer notebook set up:

julia> using IJulia

julia> notebook()

Either way, you will be prompted to install jupyter or jupyterlab via Conda. It is highly recommended to select yes (y) and proceed.

Once everything is installed, you can open Jupyter in your favorite web browser. From here, navigate to the repository where the tutorials are stored and enjoy the tutorials!

Installation Tips

If you want Jupyter running in the background, provide the detached=true argument within either notebook or jupyterlab. I.e:

julia> using IJulia

julia> notebook(detached=true)

julia> using IJulia

julia> jupyterlab(detached=true)

This frees the Julia REPL from being stuck on a Jupyter process and puts it in the background.

Tutorial Index

Here is a list of available tutorials based around sections that come from the Introduction to Linear Algebra textbook [1]:

Section 1: Introduction to Vectors

Section 1.1: Vectors and Linear Combination - How linear combination operates. How to think geometrically about vectors.
Section 1.2: Lengths and Dot Products - How to find the dot product of two given vectors. Discussion about the special results of a dot product. How to find the length of a vector and its characteristics.
Section 1.3: Matrices - Introduction to matrices and matrix equations.

Section 2: Solving Linear Equations

Section 3: Vector Spaces and Subspaces

Section 4: Orthogonality

Section 5: Determinants

Section 6: Eigenvalues and Eigenvectors

Section 7: The Singular Value Decomposition (SVD)

Section 8: Linear Transformations

Section 9: Complex Vectors and Matrices

Section 10: Applications

Section 11: Numerical Linear Algebra

Section 12: Linear Algebra in Probability & Statistics

Misc

Julia Tips

If one does not want to have to remember to activate the Julia environment whenever activating their REPL in the tutorial directory, one can appened this to their startup.jl file:

using Pkg

if isfile("Project.toml") && isfile("Manifest.toml")
    Pkg.activate(".")
end

It will automatically activate an environment based on present project .toml files. [2]

References

[1] G. Strang, Introduction to Linear Algebra, 5th ed. Wellesey - Cambridge Press, 2016.

[2] Bogumił Kamiński, “Activating project environment in Julia REPL automatically,” May 10, 2020. https://bkamins.github.io/julialang/2020/05/10/julia-project-environments.html (accessed Jun. 18, 2020).

TheCedarPrince / LinAlgTuts.jl

readme