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This course is all about matrices and covers the linear algebra that every engineer should know in a nutshell. This course's mathematics is presented at the level of an advanced high school student, but students should typically take this course after completing a university-level single variable calculus course. This course contains no derivatives or integrals, but students are expected to have a sufficient level of mathematical maturity. Nonetheless, anyone interested in learning the fundamentals of matrix algebra is welcome to join.
Syllabus :
1. Matrices
- Definition of a Matrix
- Addition and Multiplication of Matrices
- Special Matrices
- Transpose Matrix
- Inner and Outer Products
- Inverse Matrix
- Orthogonal Matrices
- Rotation Matrices
- Permutation Matrices
2. Systems of linear Eqations
- Gaussian Elimination
- Reduced Row Echelon Form
- Computing Inverses
- Elementary Matrices
- LU Decomposition
- Solving (LU)x = b
3. Vector Spaces
- Vector Spaces
- Linear Independence
- Span, Basis and Dimension
- Gram-Schmidt Process
- Gram-Schmidt Process Example
- Null Space
- Application of the Null Space
- Column Space
- Row Space, Left Null Space and Rank
- Orthogonal Projections
- The Least-Squares Problem
- Solution of the Least-Squares Problem
4. Eigenvalues and Eigenvectors
- Two-by-Two and Three-by-Three Determinants
- Laplace Expansion
- Leibniz Formula
- Properties of a Determinant
- The Eigenvalue Problem
- Finding Eigenvalues and Eigenvectors
- Matrix Diagonalization
- Matrix Diagonalization Example
- Powers of a Matrix
- Powers of a Matrix Example
