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Linear Algebra Basics
  • Level Professional
  • Duration 21 hours
  • Course by IIT Roorkee
  • Offered by

About

Machine learning and data science are the most popular topics of research nowadays. They are applied in all the areas of engineering and sciences. Various machine learning tools provide a data-driven solution to various real-life problems. Basic knowledge of linear algebra is necessary to develop new algorithms for machine learning and data science. In this course, you will learn about the mathematical concepts related to linear algebra, which include vector spaces, subspaces, linear span, basis, and dimension. It also covers linear transformation, rank and nullity of a linear transformation, eigenvalues, eigenvectors, and diagonalization of matrices. The concepts of singular value decomposition, inner product space, and norm of vectors and matrices further enrich the course contents.

Modules

Course Introduction

    • 1 Readings
    • 1 Discussion
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1 Discussions

  • Meet and Greet

1 Readings

  • Course Overview

Real Vector Space

    • 6 Videos
    • 2 Readings
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6 Videos

  • Binary Operations
  • Vector Space - I
  • Vector Space - II
  • Vector Subspace
  • Linearly Dependence and Independence of Vectors
  • Linear Combination and Linear Span of Vectors

2 Readings

  • Essential Reading: Real Vector Space
  • Recommended Reading: Real Vector Space

Practice Quiz

    • 1 Assignment
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1 Assignment

  • Practice Quiz: Week 1

Graded Quiz

    • 1 Assignment
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1 Assignment

  • Graded Quiz: Week 1

Basis and Dimension of a Vector Space

    • 1 Videos
    • 1 Readings
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1 Videos

  • Basis and Dimension of a Vector Space

1 Readings

  • Essential Reading: Basis and Dimension of a Vector Space

Linear Transformations

    • 4 Videos
    • 2 Readings
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4 Videos

  • Linear Transformations
  • Null Space of a Linear Transformation
  • Range Space of a Linear Transformation
  • Matrix Associated with a Linear Transformation

2 Readings

  • Essential Reading: Linear Transformations
  • Recommended Reading: Linear Transformations

Eigenvalues of a Matrix

    • 1 Videos
    • 2 Readings
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1 Videos

  • Eigenvalues of a Matrix

2 Readings

  • Essential Reading: Eigenvalues of a Matrix
  • Live Session 1

Practice Quiz

    • 1 Assignment
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1 Assignment

  • Practice Quiz: Week 2

Graded Quiz

    • 1 Assignment
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1 Assignment

  • Graded Quiz: Week 2

Diagonalizable Matrices

    • 6 Videos
    • 3 Readings
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6 Videos

  • Eigenvector of a Matrix
  • Special Matrices and Their Properties
  • Similar Matrices
  • Diagonalizable Matrices - I
  • Diagonalizable Matrices - II
  • Applications of Diagonalization of a Matrix

3 Readings

  • Essential Reading: Diagonalizable Matrices
  • Recommended Reading: Diagonalizable Matrices
  • Live Session 2

Practice Quiz

    • 1 Assignment
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1 Assignment

  • Practice Quiz: Week 3

Graded Quiz

    • 1 Assignment
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1 Assignment

  • Graded Quiz: Week 3

Spectral Decomposition and Singular Value Decomposition

    • 4 Videos
    • 2 Readings
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4 Videos

  • Spectral Decomposition
  • Singular Value Decomposition - I
  • Singular Value Decomposition - II
  • Applications of Singular Value Decomposition

2 Readings

  • Essential Reading: Spectral Decomposition and Singular Value Decomposition
  • Recommended Reading: Spectral Decomposition and Singular Value Decomposition

Inner Product and Vector Norms

    • 2 Videos
    • 2 Readings
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2 Videos

  • Inner Product Space
  • Vector and Matrix Norms

2 Readings

  • Essential Reading: Inner Product and Vector Norms
  • Live Session 3

Practice Quiz

    • 1 Assignment
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1 Assignment

  • Practice Quiz: Week 4

Graded Quiz

    • 1 Assignment
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1 Assignment

  • Graded Quiz: Week 4

Staff-Graded Assignment

    • 3 Readings
    • 1 Lab
    • 1 Assignment
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1 Assignment

  • Linear Algebra Basics Using Python

1 Labs

  • Jupyter Lab for Assignment

3 Readings

  • How to Attempt and Submit the Assignment
  • Introduction to Python for Linear Algebra
  • How to Use Coursera Jupyter Lab

Auto Summary

Explore the fundamentals of Linear Algebra in this professional-level course designed for Data Science and AI enthusiasts. Led by Coursera, the course delves into essential mathematical concepts, including vector spaces, eigenvalues, linear transformations, and more. With a comprehensive 1260-minute duration, learners can choose from Starter or Professional subscription options. Ideal for those aiming to enhance their machine learning and data science skills.

Dr. S. K. Gupta
Instructor

Dr. S. K. Gupta