Scalars, Vectors, Matrices, and Tensors
Vector Norms
Matrix Norms (Frobenius Norm)
Dot Product and Inner Products
Hadamard Product (Element-wise multiplication)
Matrix Multiplication
Matrix Transpose and Trace
Identity and Diagonal Matrices
Symmetric and Orthogonal Matrices
Matrix Inversion and Moore-Penrose Pseudoinverse
Determinants
Linear Independence and Dependence
Span and Basis
Vector Subspaces (Null Space, Column Space, Row Space)
Linear Transformations and Mappings
Affine Transformations
Matrix Rank
Orthogonal Projections
Gram-Schmidt Process
Systems of Linear Equations (Gaussian Elimination)
Eigenvalues and Eigenvectors
Eigendecomposition
Singular Value Decomposition (SVD)
LU Decomposition
QR Factorization
Cholesky Decomposition
Matrix Approximation and Low-Rank Approximation
Positive Definiteness and Semi-definiteness
Quadratic Forms
The Jacobian Matrix
The Hessian Matrix
Cosine Similarity
Change of Basis
