What you will learn
- Master singular value decomposition (SVD) and its applications
- Learn advanced matrix factorizations (LU, QR, Cholesky)
- Solve least squares problems with regularization
- Apply eigenvalue methods to dynamical systems
- Develop computational linear algebra skills in MATLAB/Python
- Analyze matrix conditioning and numerical stability
Program Overview
Matrix Factorizations
⏱️ 4-5 weeks
- LU decomposition with pivoting
- QR decomposition (Gram-Schmidt vs. Householder)
- Cholesky for symmetric matrices
- Applications to linear systems
Singular Value Decomposition
⏱️ 5-6 weeks
- Theory behind SVD
- Low-rank approximations
- Pseudoinverses and least squares
- Applications to data compression
Eigenvalue Methods
⏱️ 4-5 weeks
- Power iteration and QR algorithm
- Spectral theorem applications
- Positive definite matrices
- Dynamical systems analysis
Special Topics
⏱️ 3-4 weeks
- Sparse matrix algorithms
- Randomized numerical linear algebra
- Matrix functions (exponentials, logarithms)
- Case studies in machine learning
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Job Outlook
- Critical for:
- Machine Learning Researchers (120K−250K)
- Computational Scientists (90K−180K)
- Quantitative Analysts (150K−350K+)
- Computer Vision Engineers (110K−220K)
- Industry Impact:
- 85% of ML papers using SVD require this knowledge
- Key skill for FAANG research positions
- Emerging Applications:
- Quantum computing simulations
- Large language model optimizations
- Biomedical imaging reconstruction
Specification: Matrix Methods By University Of Minnesota
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