🔢 Linear Algebra Core Topics
1. Vectors
- Definition & Notation
- Vector Operations (Addition, Scalar Multiplication)
- Dot Product & Cross Product
- Magnitude & Direction
- Linear Independence
2. Matrices
- Matrix Types (Square, Diagonal, Identity, Zero, etc.)
- Matrix Operations (Addition, Multiplication, Transpose)
- Inverse & Determinant of a Matrix
- Matrix Rank
- Elementary Row Operations
3. Systems of Linear Equations
- Representing Systems with Matrices
- Row Echelon Form (REF) and Reduced Row Echelon Form (RREF)
- Gaussian & Gauss-Jordan Elimination
- Consistency of Systems
4. Vector Spaces
- Subspaces
- Basis & Dimension
- Column Space, Row Space, Null Space
- Linear Transformations
5. Eigenvalues & Eigenvectors
- Definition & Calculation
- Characteristic Polynomial
- Diagonalization
- Applications in Stability, PCA, etc.
6. Advanced Concepts
- Orthogonality & Orthogonal Projections
- Gram-Schmidt Process
- Singular Value Decomposition (SVD)
- Change of Basis
📈 Applications
- Machine Learning (PCA, least squares)
- Computer Graphics (Transformations)
- Cryptography
- Quantum Computing
- Network Analysis
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