What you will learn
- Master vector/matrix operations and properties
- Understand linear transformations and their geometric interpretations
- Solve systems of equations using matrix methods (Gaussian elimination, LU decomposition)
- Learn eigenvalues/eigenvectors with practical applications
- Develop mathematical reasoning and proof-writing skills
- Gain computational skills using tools like MATLAB or Python (implementation varies by institution)
Program Overview
Vectors and Matrices
⏱️ 3-4 weeks
- Vector spaces and subspaces
- Matrix algebra and special matrices
- Linear independence and basis
- Dot products and orthogonality
Linear Systems
⏱️ 3-5 weeks
- Gaussian elimination
- Matrix inverses and determinants
- LU and QR factorizations
- Applications to circuit analysis and optimization
Transformations
⏱️ 4-5 weeks
- Matrix representations of linear transformations
- Change of basis
- Image and kernel spaces
- Geometric transformations (rotations, projections)
Eigen-theory
⏱️ 4-6 weeks
- Characteristic polynomials
- Diagonalization
- Spectral theorem
- Applications to dynamical systems
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Job Outlook
- Essential for:
- Machine Learning (85% of roles require LA)
- Computer Graphics/Game Development
- Quantum Computing
- Engineering Simulations
- Salary Boost:
- STEM roles requiring linear algebra pay 18-25% premium
- Advanced Study:
- Required for graduate programs in CS, Physics, and Applied Math
Specification: Introduction to Linear Algebra
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