Linear Algebra · Overview
Course Topics
An introduction to linear algebra covering vector spaces, matrix theory, linear transformations, and eigenvalue problems — with applications across mathematics, science, and engineering.
1
Systems of Linear Equations
Row reduction, echelon forms, solution sets
Week 1–2 →
2
Matrix Algebra
Operations, transpose, inverses
Week 3
3
Determinants
Cofactor expansion, properties, Cramer's rule
Week 4
4
Vector Spaces
Subspaces, null space, column space, bases
Week 5–6
5
Eigenvalues & Eigenvectors
Characteristic equation, diagonalization
Week 7–8
6
Orthogonality & Least Squares
Inner products, projections, Gram-Schmidt
Week 9
7
Symmetric Matrices & Quadratic Forms
Spectral theorem, positive definiteness
Week 10
8
Linear Transformations
Kernel, range, matrix representations
Week 11
9
Singular Value Decomposition
SVD, pseudoinverse, low-rank approximation
Week 12
10
Applications of Linear Algebra
PCA, Markov chains, computer graphics, networks
Week 13–14