MA1101R: Linear Algebra I
AY2012/2013, Semester 1, Lecturer: Ng Kah Loon
Course Coverage:
1. Linear Systems & Elementary Row Operations
2. Row-echelon Forms & Gauss-Jordan Elimination
3. Matrices
4. Determinants
5. Euclidean n-Spaces
6. Ranks & Nullities
7. Eigenvalues & Eigenvectors
8. Diagonalization
9. Orthogonal & Orthonormal Bases
10. Best Approximations
11. Orthogonal Matrices & Diagonalizations
12. Linear Transformations
13. Ranges & Kernels
This was the most challenging course for me in my entire university life. The content covers significant breadth and depth in mathematical computation and analysis. The first few topics focus on computing matrices and linear systems using Gaussian Elimination, and the later topics will introduce the Euclidean space rigorously.
The first most important topic is the Gaussian Elimination algorithm which is used to solve linear system of equations in an algorithmic manner. It is extremely useful in computational mathematics as it is the basis for many advance algorithms and it can be implemented in MATLAB to solve for numerical solutions when many iterations are required. This topic is then followed by matrix operations such as addition, multiplication, inverse and transposition will be reviewed with greater mathematical rigor, general formula for determinant will be introduced alongside m x n matrices. Basically, everything that was taught in secondary school is now extended to n-dimensions and general formulas.
With the introduction of the Euclidean n-spaces, abstract thinking is very much necessary. Abstract notions of linear combinations, linear span and linear independence are introduced and extended to construct the bases of Euclidean subspaces. Ranks and nullities are then introduced to identify linear independence. Advanced topic such as eigenvalues, orthogonality, linear transformation, range and kernel which are techniques heavily employed in a wide range of applications from operation research to computer science to engineering will round up the course for the semester.
Overall, this course provides a strong foundation for courses that require multivariate analysis and computations. Content is pretty heavy and hence consistent work is required to understand everything. The heavy content coupled with my laziness in year 1 proves to be a disaster in the end. However, it still provided me an edge over many of my peers in economics in general equilibrium theory and dynamic optimization models despite my nightmarish results. As much as I dreaded the process of understanding most of the theorems, I did learn a lot from this module!
Workload: Moderate
Difficulty: Difficult
Grade: C
Course Coverage:
1. Linear Systems & Elementary Row Operations
2. Row-echelon Forms & Gauss-Jordan Elimination
3. Matrices
4. Determinants
5. Euclidean n-Spaces
6. Ranks & Nullities
7. Eigenvalues & Eigenvectors
8. Diagonalization
9. Orthogonal & Orthonormal Bases
10. Best Approximations
11. Orthogonal Matrices & Diagonalizations
12. Linear Transformations
13. Ranges & Kernels
This was the most challenging course for me in my entire university life. The content covers significant breadth and depth in mathematical computation and analysis. The first few topics focus on computing matrices and linear systems using Gaussian Elimination, and the later topics will introduce the Euclidean space rigorously.
The first most important topic is the Gaussian Elimination algorithm which is used to solve linear system of equations in an algorithmic manner. It is extremely useful in computational mathematics as it is the basis for many advance algorithms and it can be implemented in MATLAB to solve for numerical solutions when many iterations are required. This topic is then followed by matrix operations such as addition, multiplication, inverse and transposition will be reviewed with greater mathematical rigor, general formula for determinant will be introduced alongside m x n matrices. Basically, everything that was taught in secondary school is now extended to n-dimensions and general formulas.
With the introduction of the Euclidean n-spaces, abstract thinking is very much necessary. Abstract notions of linear combinations, linear span and linear independence are introduced and extended to construct the bases of Euclidean subspaces. Ranks and nullities are then introduced to identify linear independence. Advanced topic such as eigenvalues, orthogonality, linear transformation, range and kernel which are techniques heavily employed in a wide range of applications from operation research to computer science to engineering will round up the course for the semester.
Overall, this course provides a strong foundation for courses that require multivariate analysis and computations. Content is pretty heavy and hence consistent work is required to understand everything. The heavy content coupled with my laziness in year 1 proves to be a disaster in the end. However, it still provided me an edge over many of my peers in economics in general equilibrium theory and dynamic optimization models despite my nightmarish results. As much as I dreaded the process of understanding most of the theorems, I did learn a lot from this module!
Workload: Moderate
Difficulty: Difficult
Grade: C