# Linear Algebra
Quote
Nothing pleases a mathematician so much as having a bunch of numbers in brackets
# Buzzwords
Dot product Cross product Subspace Linear independence Nullspace Column space SVD PCA Gram-Schmidt RREF# Matrices and their properties
You should know how to manipulate em
# Analytical geometry
If your drawing skills leave much to be desired, analytical geometry will help with defining lines and planes analytically
# Matrix subspaces
Any matrix can be treated as a transformation from one space to another. Knowledge of the properties of four fundamental matrix subspaces might come in handy
# Special Matrices and Factorization
Sometimes it might be beneficial to represent a matrix as a product of several matrices. This can help to speed-up computation, and to uncover hidden structure
Here are some cool matrices:
- Identity matrix
- Diagonal matrices
- Triangular matrices
- Symmetric matrices
- Skew-symmetric matrices
- Orthogonal matrices
- Rotation matrices
# Change of basis
Sometimes it is necessary to have a different perspective on things. Change of basis can help to find out where
# Applications
- Computer Vision
- Navigation
# Projections
Projections are like shadows
# Applications
- Computer Vision
- Optimization
# Eigendecomposition SVD and PCA
Methods to extract the most important information
# Applications
- Pseudoinverse
- Least squares optimization
- Data compression
- Signal processing
- Recommendation systems
- Face recognition
# Cholesky factorization
The method to speedup numerical calculations and equations solving
# Applications
- Matrix inversion
- Equation solving
- Newton's method for non-linear optimization
- Kalman filters
- Monte-Carlo simulations