Department of Mathematicscoretheory
COMPUTATIONAL LINEAR ALGEBRA
MAT 2135
Syllabus
- 01Introductory Example: Linear Models in Economics and Engineering
- 02Systems of Linear Equations
- 03Row Reduction and Echelon Forms
- 04Vector Equations
- 05The Matrix Equation Ax = b
- 06Solution Sets of Linear Systems
- 07Applications of Linear Systems
- 08Linear Independence
- 09Introduction to Linear Transformations
- 10The Matrix of a Linear Transformation
- 11Linear Models in Business, Science, and Engineering
- 12Matrix Algebra
- 13Partitioned Matrices
- 14Matrix Factorizations
- 15Subspaces of Rn
- 16Dimension and Rank
- 17Vector Spaces
- 18Vector Spaces and Subspaces
- 19Null Spaces, Column Spaces, and Linear Transformations
- 20Linearly Independent Sets
- 21Bases
- 22The Dimension of a Vector Space
- 23Applications to Difference Equations
- 24Eigenvectors and Eigenvalues
- 25The Characteristic Equation
- 26Diagonalization
- 27Inner Product Spaces
- 28Orthogonal Projections
- 29The Gram-Schmidt Process
- 30Least-Squares Problems
- 31Determinants, Diagonalization of Symmetric Matrices
- 32Quadratic Forms
- 33Constrained Optimization
- 34The Singular Value Decomposition
References
- S. Kumarasen, Linear Algebra, Geometric approach, PHI, 2017
- R. Rao and P. Bhimsankaram: Linear algebra, Hindustan book agency, 2000
- S. H. Friedberg, A. J. Insel and L. E. Spence: Linear algebra, Pearson, 2015
- D. C Lay: Linear algebra and its applications, Pearson, 2014
Credits Structure
3Lecture
1Tutorial
0Practical
4Total