MIT 18.06
System of Equations
- Singularity / Non Singularity
- Linear Dependence / Independence
- Determinant
Eliminations
- Solve a system of linear equations (Matrix Row Reduction)
- Row operations preserves singularity
- Associative
- Row echelon form
- Rank
- Gaussian Elimination Algorithm
Vector Algebra
- Vector Operations
- Dot product
- Geometric dot product
- Multiply a matrix by vector
- Linear Transformation Properties
- Matrix Multiplication
- Identity Matrix
- Matrix Inverse
- Neural Network
Determinants in-depth
- Dimension of linear transformation = rank
- determinant = area of span
- det(AxB) = det(A) x det(B)
Eigen Value
- Basis is a set of vectors that:
- spans a vector space
- is linearly independent
- Eigenvectors: direction of stretch
- Eigenvalues: how much to stretch
- Eigenbasis: the set of a matrix's eigenvectors, can be arranged as a matrix with one eigenvector in each column