This course is a basic course offered to UG/PG students of Engineering/Science background. It contains basics of matrix algebra, computer arithmetic, conditioning and condition number, stability of numerical algorithms, vector and matrix norms, convergent matrices, stability of non-linear systems, sensitivity analysis, singular value decomposition (SVD), algebraic and geometric properties of SVD, least square solutions, Householder matrices and applications, QR method, Power method and applications, Jacobi method for finding the eigenvalues of a given matrix. This course has tremendous applications in diverse fields of Engineering and Sciences such as control theory, image processing, numerical analysis and dynamical systems etc.
Week 1: Matrix operations and type of matrices, Determinant of a Matrix, Rank of a matrix, Vector Space-I, Vector Space-II
Week 2: Linear dependence and independence, Bases and Dimensions – I, Bases and Dimension - II, Linear Transformation - I, Linear Transformation - II
Week 3: Orthogonal subspaces, Row space, column space and null Space, Eigenvalues and Eigenvectors-I, Eigenvalues and Eigenvectors-II, Diagonalizable Matrices
Week 4: Orthogonal Sets, Gram Schmidt orthogonalization and orthonormal bases, Introduction to Matlab, Sign integer representationComputer representation of numbers
Week 5: Floating point representation, Round-off error, Error propagation in computer arithmetic, Addition and multiplication of floating point numbers, Conditioning and condition numbers-I
Week 6: Conditioning and condition numbers-II, Stability of numerical algorithms-I, Stability of numerical algorithms-II, Vector norms - I, Vector norms - II
Week 7: Matrix Norms - I, Matrix Norms-II, Convergent Matrices - I, Convergent Matrices - II, Stability of non-linear system
Week 8: Condition number of a matrix: Elementary properties, Sensitivity analysis-I, Sensitivity analysis-II, Residual theorem, Nearness to singularity
Week 9: Estimation of the condition number, Singular value decomposition of a matrix – I, Singular value decomposition of a matrix - II, Orthogonal Projections, Algebraic and geometric properties of matrices using SVD
Week 10: SVD and their applications, Perturbation theorem for singular values, Outer product expansion of a matrix, Least square solutions-I, Least square solutions-II
Week 11: Psudeo - inverse and least square solution, Householder matrices and their applications, Householder QR factorization –I, Householder QR factorization –II, Basic theorems on eigenvalues and QR method
Week 12: Power method, Rate of convergence of Power method, Applications of Power method with shift, Jacobi method-I, Jacobi method-II
MOOCs stand for Massive Open Online Courses. These arefree online courses from universities around the world (eg. StanfordHarvardMIT) offered to anyone with an internet connection.
How do I register?
To register for a course, click on "Go to Class" button on the course page. This will take you to the providers website where you can register for the course.
How do these MOOCs or free online courses work?
MOOCs are designed for an online audience, teaching primarily through short (5-20 min.) pre recorded video lectures, that you watch on weekly schedule when convenient for you. They also have student discussion forums, homework/assignments, and online quizzes or exams.