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Josiah's Math Notes

Linear Algebra

"Linear algebra is the branch of mathematics concerning linear equations."

"Linear algebra is the study of lines and planes, vector spaces and mappings that are required for linear transforms. It is a relatively young field of study, having initially been formalized in the 1800s in order to find unknowns in systems of linear equations."

I have compiled this series of notes mostly by watching the lectures by Professor Gilbert Strang posted on MIT OpenCourseware. As of right now theses notes are not complete, however I do plan on revising them in the future.

Pages

1. Fundamental Subspaces, Guass-Jordan Elimation, Projections, Orthogonality, Gram-Schmidt, Determinants, Cramer's rule
2. Eigenvalues, Eigenvectors, Systems of Differential Equations, and Dynamic Systems
3. Markov Matrices, Fourier Series, Fast Fourier Transform
4. Symmetric Matrices, Positive Definite Matrices, Similar Matrices, Jordan Form, Single Value Decomposition, Linear Transformations, Change of Basis, Application: Image Compression
5. Application: Linear Algebra in Roblox
6. Miscellaneous Topics