The course of Analytical Geometry and Linear Algebra 2 for 1st year bachelor students in Innopolis University in 2023 year.
This repository contains regularly updated course materials. You can use lab slides for self study. They are created in such manner, that almost 90% of material can be understood without teacher.
- Lab 1 (The geometry of linear equation, Gaussian elimination, Matrix notation and matrix multiplication)
- Lab 2 (Gaussian elimination recap, A=LU, A=LDV, PA=LU factorization)
- Lab 3 (Null space)
- Lab 4 (Quiz, Four Fundamental Subspaces)
- Lab 5 (Projection, Application (Least Squares))
- Lab 6 (Orthogonality + OrthoNormality + SO(3); Gram-Schmidt; Quiz)
- Lab 7 (Eigenvalues and Eigenvectors; Diagonalization of a Matrix (Спектральное разложение); Fast A$^N$ calculation)
- Lab 8 (Complex numbers; Complex matrices; Hermitian and Unitary matrices)
- Lab 9 (System of linear differential equations)
- Lab 10 (Symmetric matrices; Positive definite matrices and minima)
- Lab 11 (Similar matrices; Singular value decomposition - SVD; Left and right inverses. Pseudoinverse)
- Lab 12 (Fast Fourier Transform (FFT); Discrete Fourier Transform (DFT); Circulant Matrix)
Pull requests with suggestions and improvements, however small or big, are welcome!
The changes in lecture slides are going through an automated check.
The PDFs are compiled and updated automatically when PR is merged. You don't need to update them manually. They are also uploaded as workflow artifacts for every new commit pushed into this repository. You can use them to see your changes.
Consider adding *.pdf to the .git/info/exclude file on your local repo. Here is the overy long but helpful description why it works
In each lab slides, you can find a reference material to the lab.