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Determinants : The Foundation of Linear Algebra (Udemy.com)

Fundamental Course in Linear Algebra for Machine Learning, Data Science, Computer Science and Electrical Engineering

Created by: Shilank Singh

Last updated March 2025

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What you will learn

  • Determinants Definition
  • Minors and Cofactors
  • Determinants Expansion
  • Properties of Determinants
  • Multiplication of Determinants
  • Differentiation and Integration of Determinants
  • Matrices Definition
  • Types of Matrices
  • Difference between a Matrix and a Determinant
  • Operations on Matrices
  • Various Kinds Of Matrices
  • Adjoint of a Square Matrix
  • Elementary Row and Column Transformation
  • Inverse of a Matrix
  • Echelon Form, Normal Form and Rank of a Matrix
  • Solution of Simultaneous Linear Equations
  • Reflection and Rotation of a Matrix

How it compares

Against the other 127 rated Udemy courses in Math on CourseDuck:

  • Rating4.3 out of 5higher than 7% of them
  • Reviews24#126 of 128 by number of reviews
  • Length2.6 hoursshorter than 86% of them
  • Last updatedMarch 2025earlier than 49% of them

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Course Description

Determinants is the introductory course of Linear Algebra as it covers all the essentials for the study of Linear Algebra. This course is vital for any student wishing to pursue a degree in Science or Engineering.

This 20+ lecture course includes video explanations of everything from Fundamental of Determinats, and it includes more than 20+ examples (with detailed solutions) to help you test your understanding along the way.

Determinants are the scalar quantities obtained by the sum of products of the elements of a square matrix and their cofactors according to a prescribed rule. They help to find the adjoint, inverse of a matrix. Further to solve the linear equations through the matrix inversion method we need to apply this concept. The cross-product of two vectors is remembered easily through the calculation of determinants.

In this course, let's learn more about the process of finding determinants of different orders and their properties, and we will work on a few solved examples.

Determinants are considered as a scaling factor of matrices. They can be considered as functions of stretching out and the shrinking in of the matrices. Determinants take a square matrix as the input and return a single number as its output.

Determinants: The Foundation of Linear Algebra is organized into the following sections:       

  • Introduction to Determinants

  • Determinants Expansion

  • Properties of Determinants

  • Multiplication of Determinants

  • Differentiation and Integration of Determinants

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Instructor Details

Shilank Singh

Hello students, I am Shilank Singh. I was born and raised in Mumbai, India. My interest in maths developed at an early age when I started attending pre-school. I attended Indian Institute of Technology, Delhi and post graduated in 2013 with a degree M.Sc. in Mathematics. In the fall of 2013, I was hired to teach Engineering Mathematics at Mumbai University and I have taught there for three years. Currently, I live in New Delhi and work as a Maths and Statistics Tutor over here since January, 2017.

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Reviews

4.3

24 ratings on Udemy

Select a bar to show only those reviews.Select the bar again to show every rating.

By Michael O'Regan on 9/11/2024

Overall, the course met my expectations. It would have benefitted from more discussion of the geometric basis of the determinant and justification of the rules for differentiation and integration of determinants, though this latter discussion would have been beyond the scope of a short course and strayed into the realms of real analysis. The course is specialist in nature and requires a good general knowledge of linear algebra and calculus on the part of the student in order to benefit. The course focusses entirely on matrix determinants and does not touch on any other aspects of matrix algebra as suggested in the overview.

By Katie Huff on 5/24/2020

It could have been much shorter. Most of the second lesson was devoted to repeating unnecessary information. The example in lesson three should maybe have been expanded into finding minors and cofactors of different sized determinants rather than finding every minor and cofactor of a single determinant.

By Deepak Tiwari on 10/1/2019

its to good to start ! thanks a lot to create this course for us!!!

By Jay Jayasinghe on 9/10/2019

Very organize. Highly trained professor.

By Dennis Cohoon on 8/29/2019

I completely enjoy this course and the effort the instructor puts in to deliver the content. But for instance in Lesson 9, Properties of Determinants, Property 5 - I finally can see what is lacking. The course is a challenge with all the equations, and particularly the introductory rules that state what is to be proven with the explanatory equations and discussion. This is a given and the instructor is great in managing this chore. But what I wish is that we not just do a numeric demonstration of the validity, but we in each section we give a graphical representation of the scenario this particular property or rule or description applies to, and further emphasize the real world problem solving technique these properties/proofs enable. Put in another way, I am putting in the effort to understand and agree with each of the proofs given, but after I chew on this content all way, I still say to myself - what in the world do I do with this knowledge; I don't understand anything about it's application, and thus I will forget all the details about this Udemy course before the real world ever asks me to apply my understanding. To summarize this course, and possibly some of your others would be beyond epic if you could add some static graphical content that derives from the visual insights being delivered by - 1brown3blue youtube channel in his series "Essence of linear algebra". By the say in the 1B3BL series, he says the opposite, the minutia of punching out the calculations can be found elsewhere. But that is the challenge of the student - to move forward with all this and gain mastery. Thank you for listening.

By Harshad Riswadkar on 4/2/2018

Good course. So far it has helped me in understanding the concept of determinants. It would be great if the sound quality of the videos can be improved and the author can speak a little faster.

By Bobbie Smith on 2/25/2018

Very interesting course. Very well presented. Shilank Singh really knows his stuff. Thank you.

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Read all 24 reviews on Udemy

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Overall Score : 86 / 100