IIT Roorkee

Linear Algebra Basics

Taught in English


Gain insight into a topic and learn the fundamentals

Dr. S. K. Gupta

Instructor: Dr. S. K. Gupta

Intermediate level
Some related experience required
21 hours to complete
3 weeks at 7 hours a week
Flexible schedule
Learn at your own pace

What you'll learn

  • Describe the vector spaces, vector subspaces, basis, and dimension of a vector space.

  • Explain the linear transformations defined on vector spaces and eigenvalues and eigenvector of a matrix, symmetric and skew-symmetric matrices.

  • Explain diagonalizable matrices, their applications and the inner product, and the norm of vectors and matrices.

Details to know

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8 quizzes, 1 assignment

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There are 6 modules in this course

This module provides an overview of the course content and structure. In this module, you will learn about the different course elements. In this module, you will get acquainted with your instructor and get an opportunity to introduce yourself and interact with your peers.

What's included

1 reading1 discussion prompt

In this module, you will learn about vector space and its subspace. Further, you will learn about the set of linearly dependent and independent vectors. You will also gain insight into the linear combination and linear span of a set of vectors.

What's included

6 videos2 readings2 quizzes

In this module, you will learn about the basis and dimension of a vector space. You will learn about the concept of linear transformations defined on real vector spaces. Further, you will understand that there is a matrix associated with each linear transformation for the bases. Finally, you will get an insight into the eigenvalues of a square matrix.

What's included

6 videos5 readings2 quizzes

In this module, you will learn about the eigenvectors corresponding to the eigenvalues of a matrix. You will then learn about the properties of special matrices (symmetric and skew-symmetric). Finally, you will learn about the concept of diagonalization of a matrix (eigen decomposition of a matrix) with its applications.

What's included

6 videos3 readings2 quizzes

In this module, you will learn about the spectral value decomposition and singular value decomposition of a matrix with some applications. Further, you will learn about the inner product space and norms of vectors and matrices with two useful identities—Cauchy-Schwarz inequality and Polarization identity—for machine learning algorithms.

What's included

6 videos4 readings2 quizzes

In this module, you are provided with your term-end project, instructions to complete the project, and the criteria for how your instructor will grade your submission.

What's included

3 readings1 assignment1 ungraded lab


Dr. S. K. Gupta
IIT Roorkee
1 Course296 learners

Offered by

IIT Roorkee

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