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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 Linear Algebra online program is a Swayam course provided by the Ministry of Education(Government of India) and is designed by the National Programme on Technology Enhanced Learning(NPTEL) and the Indian Institute of Science in Bangalore. This course is part of the mathematics domain and will take twelve weeks for the students to complete the training.

The course instruction is done by Prof. Dilip. P. Patil, a faculty member of the department of mathematics in IISC. The course materials that include books, references, and assignments will be a source of extensive learning of the subject.

The Linear Algebra training provides expertise that enables students to equip themselves with valuable mathematical insights that improve their job skills. The students of this course will develop their knowledge of the geometric concepts involved in mathematical applications and other algebraic principles. This core course will fetch the candidates three credit points and a certificate from Swayam that is recognized by NPTEL and IISC Bangalore.

The Highlights

Online mode
Twelve weeks program
Three credit points
Core course
IISC faculty
Undergraduate or postgraduate level
Free course access
Certificate

Programme Offerings

videos
Lectures
Books
references
assignments
exams
course certificate
Free training
Professional educators
Mentorship
Credits.

Courses and Certificate Fees

Fees Informations	Certificate Availability	Certificate Providing Authority
INR 1000	yes	IISc Bangalore

The candidates of the ‘‘Linear Algebra’ certification course can access the course without any payment but are required to pay the registration fee for the final exam and course certificate.

Linear Algebra fee structure

Course	Amount in INR
Fee	Nil
Exam and certificate fee	Rs 1000

Eligibility Criteria

The candidates who have prior knowledge of the language of set theory and the concepts of elementary algebra and calculus can apply for the ‘Linear Algebra’ certification course.

Certification qualifying details

The candidate has to score a minimum of 10out of 25 in the assignments and 30 out of 75 in the final exam to become eligible for the course certificate issued by Swayam which is authenticated by NPTEL and IISC.

What you will learn

Mathematical skill

The linear algebra training will help the students develop mathematical skills and knowledge about algebraic linear operations, geometric assumptions, and the calculation of vector space and inner products along with solving problems related to it. The students will get familiar with the multilinear forms theory and determinants along with the principles of significant ideas of linear algebra.

Who it is for

Research Associate

The course on ‘Linear Algebra’ benefits the graduates, post-graduate students, and research students of science and engineering and provides the required skills to become experts in the domain.

Admission Details

For the registration of the ‘Linear Algebra’ training program, the students will have to apply online through the official website of Swayam.

Step 1: Go to the course page on the Swayam website using the link below,

https://onlinecourses.nptel.ac.in/noc21_ma50/preview

Step2: Select the registration link and the page opens

Step 3: Fill in the relevant information and complete the process.

Application Details

The applicants will have to enter their name and email address or sign up for the courses using their Google, Facebook, or Microsoft account credentials, on the registration form for admission.

The Syllabus

Introduction to Algebraic Structures - Rings and Fields.
Definition of Vector Spaces.
Examples of Vector Spaces.
Definition of subspaces.
Examples of subspaces.

Examples of subspaces (continued).
Sum of subspaces.
System of linear equations.
Gauss elimination.
The generating system, linear independence, and bases.

Examples of a basis of a vector space.
Review of univariate polynomials.
Examples of univariate polynomials and rational functions.
More examples of a basis of vector spaces.
Vector spaces with the finite generating system.

Steinitz’s exchange theorem and examples.
Examples of finite-dimensional vector spaces.
Dimension formula and its examples.
Existence of a basis.

Existence of a basis.
Introduction to Linear Maps.
Examples of Linear Maps.
Linear Maps and Bases.
Pigeonhole principle in Linear Algebra.

Interpolation and the rank theorem.
Examples.
Direct sums of vector spaces.
Projections.
Direct sum decomposition of a vector space.

Dimension equality and examples.
Dual spaces.
Dual spaces (continued).
Quotient spaces.
Homomorphism theorem of vector spaces.

Isomorphism theorem of vector spaces.
Matrix of a linear map.
Matrix of a linear map (continued).
Matrix of a linear map (continued).
Change of bases.

Computational rules for matrices.
The rank of a matrix.
Computation of the rank of a matrix.
Elementary matrices.
Elementary operations on matrices.

LR decomposition.
Elementary Divisor Theorem.
Permutation groups.
Canonical cycle decomposition of permutations.
Signature of a permutation.

Introduction to multilinear maps.
Multilinear maps (continued).
Introduction to determinants.
Determinants (continued).
Computational rules for determinants.

Properties of determinants and adjoint of a matrix.
Adjoint-determinant theorem.
The determinant of a linear operator.
Determinants and Volumes.
Determinants and Volumes (continued)

Evaluation process

The candidates will have to take up the final proctored exam and clear with a minimum score of 75% to receive the ‘Linear Algebra’ certification from Swayam. The registration for the exam has to be done through the website and the course fee has to be paid to write the exam in allocated exam centers.