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Quick Facts
| Medium Of Instructions | Mode Of Learning | Mode Of Delivery |
|---|---|---|
| English | Self Study | Video and Text Based |
Course Overview
The Numerical Linear Algebra online course has been structured as a basic and fundamental course for the students who are pursuing their postgraduate or undergraduate level degree course from the stream of science or engineering.
The Numerical Linear Algebra certification benefits the registered students by providing them the core concepts regarding- stability of numerical algorithms, matrix algebra, stability of nonlinear systems, conditioning and condition number, vector and matrix norms, convergent matrices, computer arithmetic, sensitivity analysis, singular value decomposition (SVD), least square solutions, algebraic and geometric properties of SVD, Power method and applications, Householder matrices and applications, QR method, Jacobi method for finding the eigenvalues of a given matrix.
The Numerical Linear Algebra certification course will be dealing with all the real world applications of the numerical linear algebra concept in the diverse fields of - sciences and engineering. The twelve weeks course will be emphasised on topics like- control theory, numerical analysis, image processing and dynamical systems.
The Highlights
- Course partnered by Indian Institute of Roorkee
- Certificate by NPTEL and Indian Institute of Roorkee
- Course organised by Swayam
- 12 weeks programme
- Certificate recognised by government
- AICTE approved FD course
Programme Offerings
- test
- online learning
- Self-assessments
- Reading Material
- videos
- case study
- Lectures
- Quiz.
Courses and Certificate Fees
| Fees Informations | Certificate Availability | Certificate Providing Authority |
|---|---|---|
| INR 1000 | yes | IIT Roorkee |
- The Numerical Linear Algebra fees for registration is absolute.
- Candidates have to pay Rs. 1,000/- for procuring the sit in examinations.
Numerical Linear Algebra fees details -
Particulars | Amount |
Registration fee | Free |
Examination fee | Rs. 1,000/- |
Eligibility Criteria
Certification Qualification Details
For the Numerical Linear Algebra training certification, it is essential for candidates to pay the fees and appear for the final proctored examination. The candidates have to clear this exam and secure a minimum 75% in the exam. They need to also achieve 25% average in 8 out of 12 assignments.
What you will learn
The students will be learning about the following in the Numerical Linear Algebra online course-
- The students will be dealing with the concept of matrix spaces.
- Candidates will be learning about the orthogonal sets.
- The concept of sign integer representation will be dealt in this course.
- The ways of representing numbers on computers will also be discussed.
- In the Numerical Linear Algebra certification syllabus, the students will study about the process of multiplying the floating numbers.
- The matrix norms will be discussed and the students will be taught its applications
- All the enrolled candidates will be taught about the residual theorem.
- The properties of geometric numbers will be elaborately explained to the students.
- Applicants will be learning about least square solutions.
- The process of estimating the conditional numbers will also be taught to the students
Who it is for
The Numerical Linear Algebra online course is for the listed students-
- Students who want to study round-off error can apply for this course.
- For the course, both UG and PG students from any technical institutions or universities or colleges can apply
Application Details
The given below steps are to be followed by the students to get their seat in the Numerical Linear Algebra training-
Step 1: Please visit the provided link to procure the application form- https://onlinecourses.nptel.ac.in/noc25_ma42/preview
Note- The session is being held and hence the application form can not be accessed. The management can hence be contacted for getting more information.
The Syllabus
- Matrix operations and type of matrices
- Determinant of a Matrix
- Rank of a matrix
- Vector Space-I
- Vector Space-II
- Linear dependence and independence
- Bases and Dimensions – I
- Bases and Dimension - II
- Linear Transformation - I
- Linear Transformation - II
- Orthogonal subspaces
- Row space
- Column space and null Space
- Eigenvalues and Eigenvectors-I
- Eigenvalues and Eigenvectors-II
- Diagonalizable Matrices
- Orthogonal Sets
- Gram Schmidt orthogonalization and orthonormal bases
- Introduction to Matlab
- Sign integer representation Computer representation of numbers
- Floating point representation
- Round-off error
- Error propagation in computer arithmetic
- Addition and multiplication of floating point numbers
- Conditioning and condition numbers-I
- Conditioning and condition numbers-II
- Stability of numerical algorithms-I
- Stability of numerical algorithms-II
- Vector norms - I
- Vector norms - II
- Matrix Norms - I
- Matrix Norms-II
- Convergent Matrices - I
- Convergent Matrices - II
- Stability of non-linear system
- Condition number of a matrix
- Elementary properties
- Sensitivity analysis-I
- Sensitivity analysis-II
- Residual theorem
- Nearness to singularity
- 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
- SVD and their applications
- Perturbation theorem for singular values
- Outer product expansion of a matrix
- Least square solutions-I
- Least square solutions-II
- 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
- Power method
- Rate of convergence of Power method
- Applications of Power method with shift
- Jacobi method-I
- Jacobi method-II