SE201 : Linear Algebra (선형대수학)
This is an introductory course on linear algebra. Linear algebra studies systems of linear equa- tions and properties of vectors and matrices, and is useful in natural science and engineering, economics, social science, and especially in machine learning and optimization. I will introduce basic concepts and properties in linear algebra and matrix theory, as well as how to compute matrix algebra by Python programming.
- Linear algebra algorithms : LU-decomposition, Gauss-Jordan elimination, Gram-Schmidt process
- Basic definition of linear algebra : rank, determinant, transformation
- Vectors and vector spaces : basis, orthogonality, orthogonal complement, column and row spaces, null and left null spaces
- Eigenvalues and eigenvectors : diagonalization, Jordan form, singular value decomposition
- Applications : solving systems of 1st order ordinary differential equations, Principal component analysis, the simplex method, natural language processing via Python.