Linear algebra for CS
Undergraduate · CS / Programming
Syllabus focus
Topics typically covered
Standard syllabus
Core linear algebra
- Vectors in R^n; dot product, norms, and angles
- Matrices, matrix multiplication, and linear maps
- Systems of equations; Gaussian elimination
- Rank, null space, and column space
- Determinants and invertibility (computational view)
Eigenmethods
- Eigenvalues and eigenvectors
- Diagonalization and spectral theorem (symmetric case)
- Orthogonality, projections, and Gram–Schmidt
- Least squares and normal equations
- Singular value decomposition (intro)
CS-facing linear algebra
- Matrix representations of graphs and Markov chains
- Least squares for fitting and overdetermined systems
- Eigenconcepts for PageRank-style iterations (intro)
- SVD intuition for dimensionality reduction
- Orthogonality in projections and QR ideas
- Numerical stability awareness for floating-point ops
STEM / applied
CS applications
- Transformations for computer graphics
- PageRank as eigenvector problem (intro)
- PCA for dimensionality reduction
- Solving linear systems in ML (normal equations, regularization)
- Numerical stability and conditioning (intro)
Computation
- Implementing matrix ops in NumPy/Python
- Sparse matrices for graphs and networks (intro)
- Iterative methods: power iteration, conjugate gradient (survey)
- GPU matrix multiply overview (intro)
- Using LA libraries vs rolling your own
Computation and ML bridges
- Implementing matrix ops efficiently (BLAS intuition)
- Sparse matrices in search and recommender systems
- PCA pipeline on a small dataset
- Linear algebra behind neural net layers (survey)
- Solving Ax=b in libraries (NumPy/SciPy/Eigen)
- Capstone: apply SVD/PCA or least squares to a CS dataset
Notes
Often cross-listed with math departments; CS sections emphasize applications over abstract proofs.