Complete Linear Algebra for Data Science & Machine Learning
4.5 (412 ratings)
Course Ratings are calculated from individual students’ ratings and a variety of other signals, like age of rating and reliability, to ensure that they reflect course quality fairly and accurately.
2,620 students enrolled

Complete Linear Algebra for Data Science & Machine Learning

Linear Algebra for Data Science, Big Data, Machine Learning, Engineering & Computer Science. Master Linear Algebra
Bestseller
4.5 (412 ratings)
Course Ratings are calculated from individual students’ ratings and a variety of other signals, like age of rating and reliability, to ensure that they reflect course quality fairly and accurately.
2,620 students enrolled
Created by Kashif Altaf
Last updated 2/2020
English
Current price: $139.99 Original price: $199.99 Discount: 30% off
5 hours left at this price!
30-Day Money-Back Guarantee
This course includes
  • 18 hours on-demand video
  • 11 articles
  • 12 downloadable resources
  • Full lifetime access
  • Access on mobile and TV
  • Certificate of Completion
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What you'll learn
  • Fundamentals of Linear Algebra and how to ace your Linear Algebra exam
  • Basics of matrices (notation, dimensions, types, addressing the entries etc.)
  • Operations on a single matrix, e.g. scalar multiplication, transpose, determinant & adjoint
  • Operations on two matrices, including addition, subtraction and multiplication of matrices
  • Performing elementary row operations and finding Echelon Forms (REF & RREF)
  • Inverses, including invertible and singular matrices, and the Cofactor method
  • Solving systems of linear equations using matrices and inverse matrices, including Cramer’s rule to solve AX = B
  • Properties of determinants, and how to perform Gauss-Jordan elimination
  • Matrices as vectors, including vector addition and subtraction, Head-to-Tail rule, components, magnitude and midpoint of a vector
  • Vector spaces, including dimensions, Euclidean spaces, closure properties and axioms
  • Linear combinations and span, spanning set for a vector space and linear dependence
  • Subspace and Null-space of a matrix, matrix-vector products
  • Basis and standard basis, and checking if a set of given vectors forms the basis for a vector space
  • Eigenvalues and Eigenvectors, including how to find Eigenvalues and the corresponding Eigenvectors
  • Basic algebra concepts ( as a BONUS)
  • And so much more…..
Course content
Expand all 210 lectures 17:53:59
+ Welcome and Introduction
1 lecture 02:43

This video is to officially welcome you to the Linear Algebra course. I give an overview of the topics covered, and the strategies to get the most out of this course!

Preview 02:43
+ Basics of Matrices
6 lectures 32:28
Matrices and their Significance - 001
02:07
Matrix Notation - 002
02:25

In this quiz, we practice how to specify the Dimensions of a Matrix.

Quiz 1: Dimensions of a Matrix
4 questions
Addressing Elements of a Matrix - 004
04:01

In this quiz, we practice how to address or refer to the elements of a matrix.

Quiz 2: Addressing Elements of a Matrix
4 questions
Solving Linear Systems in 2 Unknowns - 005
12:18

In this quiz, we practice how to solve systems of 2 linear equations in 2 unknowns, without using matrices.

Quiz 3: Solving Linear Systems in 2 Unknowns
3 questions
Solving Linear Systems in 3 Unknowns - 006
08:17

In this quiz, we practice how to solve systems of 3 linear equations in 3 unknowns, without using matrices.

Quiz 4: Solving Linear Systems in 3 Unknowns
3 questions
+ Basics of Matrices (Continued)
12 lectures 01:18:49
IMPORTANT - This section is OPTIONAL
00:13
Types of Matrices
06:13
Multiplication of Scalars with Matrices
02:16
Multiplication of two Matrices
18:29
Inverse and Determinant of a 2x2 Matrix
05:07
The Formula: Inverse (A) = Adjoint (A) / Determinant (A)
04:12
* EXAMPLE - Inverse of a 2x2 Matrix
03:22
Using Matrices to Solve Simultaneous Linear Equations
10:29
* EXAMPLE - Using Matrices to Solve Simultaneous Linear Equations
07:40
CHALLENGE QUESTION - Using Matrices to Solve Simultaneous Linear Equations
02:29
SUMMARY
10:41
+ Matrices and Systems of Linear Equations
7 lectures 46:36

https://matrix.reshish.com/

The Online Matrix Calculator: A FREE Tool
06:20

In this lesson of the Linear Algebra course, we look at how to represent a system of 2 linear equations in the 2x2 Matrix form.

Preview 08:38

In this lesson of the Linear Algebra course, we look into how to write a system of 3 linear equations in the form of a 3x3 matrix and solve it.

Systems of Linear Equations - Continued
06:40

In this lesson of the Linear Algebra course, we see how to perform different types of row operations on a matrix to convert it into Row Echelon Form (REF).

Elementary Row Operations
10:27

In this lesson of the Linear Algebra course, we learn what the Row Echelon Form (REF) of a matrix is, and how to compute it.

Row Echelon Form (REF)
10:25

In this lesson of the Linear Algebra course, we learn what the Reduced Row Echelon Form (RREF) of a matrix is, and how to obtain it.

Reduced Row Echelon Form (RREF)
03:58
* ASSIGNMENT 1: Matrices and Linear Equations
00:08
+ Matrix Algebra and Operations
5 lectures 21:24

In this lesson of the Linear Algebra course, we learn how to perform addition and subtraction of matrices.

Matrix Algebra - Addition and Subtraction
04:09

In this lesson of the Linear Algebra course, we learn how a scalar can be multiplied to a matrix, and what are the rules for that.

Matrix Algebra - Scalar Multiplication
01:44

In this lesson of the Linear Algebra course, multiplication of two matrices with each other is explained, using examples.

Preview 10:09

In this lesson of the Linear Algebra course, we learn how to get transpose of a given matrix.

Transpose of a Matrix
05:14
** ASSIGNMENT 2: Matrix Algebra & Operations
00:08
+ Determinant of a Matrix
4 lectures 20:43

In this lesson of the Linear Algebra course, we learn how to compute determinant of a 2x2 matrix.

Determinant of a 2x2 Matrix
05:27

In this lesson of the Linear Algebra course, we learn how to compute determinant of a 3x3 matrix.

Preview 12:54

In this lesson of the Linear Algebra course, I discuss some shortcuts that we can possibly use in certain cases to find determinants quickly and easily.

Finding Determinants Quickly
02:14
*** ASSIGNMENT 3: Computing Determinants
00:08
+ Inverse of a Matrix
7 lectures 46:30

In this lesson of the Linear Algebra course, we learn why inverse can be calculated only for square matrices, and why inverse doesn't exist for non-square matrices.

Inverse exists only for Square Matrices
04:24

In this lesson of the Linear Algebra course, we learn what the term Singular Matrix means, and how is it related to the inverse of a matrix.

Singular Matrices
03:58

In this lesson of the Linear Algebra course, we see why finding inverse of the coefficient matrix is important and helpful for solving a linear system.

Importance of Inverse in solving Linear Systems
06:25
Inverse of a 2x2 Matrix
00:06
Inverse of a 3x3 Matrix - The Two Methods
02:38
Inverse of a 3x3 Matrix - The Co-factor Method
11:39
Inverse of a 3x3 Matrix - Gauss-Jordan Elimination Method
17:20
+ Properties of Determinants
6 lectures 14:57

In this lesson of the Linear Algebra course, we look at the property of the determinants that deals with the matrix row operation 1.

Properties of Determinants - Row Operation 1
01:21

In this lesson of the Linear Algebra course, we look at the property of the determinants that deals with the matrix row operation 2.

Properties of Determinants - Row Operation 2
01:38

In this lesson of the Linear Algebra course, we look at the property of the determinants that deals with the matrix row operation 3.

Properties of Determinants - Row Operation 3
01:59

In this lesson of the Linear Algebra course, we summarize the properties of the determinants that deal with the matrix row operations.

Properties of Determinants - All Row Operations
01:19

In this lesson of the Linear Algebra course, we apply our knowledge of the properties of determinants.

Properties of Determinants - Row Operations Applied
04:57

In this lesson of the Linear Algebra course, we look at one more property of the matrix determinants that is very helpful..

Properties of Determinants - Another Property
03:43
+ *** OPTIONAL: Introduction to Vectors
11 lectures 52:30
Introduction to the Section
00:42
Scalars and Vectors
05:26
Geometrical Representation of Vectors
04:35
Vector Addition and Subtraction
04:31
Laws of Vector Addition and Head to Tail Rule
10:31
Unit Vector
06:54
Components of a Vector in 2D
03:07
Position Vector
04:25
3-D Vectors and Magnitude of a Vector
04:42
Displacement Vector
03:24
Finding Midpoint using Vectors
04:13
+ Vector Spaces
9 lectures 40:04

In this lesson of the Linear Algebra course, you are introduced to the Vector Spaces.

Introduction to Vector Spaces
00:56

In this lesson of the Linear Algebra course, we discuss what Euclidean vector spaces are.

Euclidean Vector Spaces - Part 1
06:10

In this lesson of the Linear Algebra course, Euclidean vector spaces are discussed in further detail, in continuation of the previous lesson.

Euclidean Vector Spaces - Part 2
04:42

In this lesson of the Linear Algebra course, further explanation is provided on the topic of Euclidean vector spaces.

Preview 05:35

In this lesson of the Linear Algebra course, we look into what Closure Properties are, and how these are used as a criteria to check for vector spaces.

Definition and Closure Properties
05:15

In this lesson of the Linear Algebra course, the ten fundamental axioms for vector spaces are listed and explained.

Axioms of Vector Spaces
04:52

In this lesson of the Linear Algebra course, examples of closure properties are discussed.

Example of Closure Properties
05:44

In this lesson of the Linear Algebra course, we discuss an example of vector spaces to clarify the concept.

Example 1 of Vector Spaces
04:34

In this lesson of the Linear Algebra course, one more example of vector spaces is discussed.

Example 2 of Vector Spaces
02:16
Requirements
  • A passion to learn about Matrices and Vectors
  • Ability to perform basic Mathematical operations (+, -, x, ÷) on numbers and fractions
  • Knowledge of how to solve a linear equation (e.g. find x in 3x-4=11)
  • Understanding of basic Algebra concepts, e.g. Powers and Roots, simplifying Fractions, Factorization, solving Equations and drawing Graphs.
  • You only need to know basic Math and Algebra to take this course.
  • And the best thing is, most of the above prerequisite topics are covered inside the course :)
Description

DO YOU WANT TO LEARN LINEAR ALGEBRA IN AN EASY WAY?

Great!

With 22+ hours of content and 200+ video lessons, this course covers everything in Linear Algebra, from start till the end!

Every concept is explained in simple language, and Quizzes and Assignments (with solutions!) help you test your concepts as you proceed.

Whether you're a student, or a professional or a Math enthusiast, this course walks you through the core concepts of Linear Algebra in an easy and fun way!



HERE IS WHAT YOU WILL LEARN:

· Fundamentals of Linear Algebra and how to ace your Linear Algebra exam

· Basics of matrices, including notation, dimensions, types, addressing the entries etc.

· Operations on a single matrix, e.g. scalar multiplication, transpose, determinant, adjoint etc.

· Operations on two matrices, including addition, subtraction and multiplication

· Performing elementary row operations and finding Echelon Forms (REF & RREF)

· Inverses, including invertible and singular matrices, and the Cofactor method

· Solving systems of equations using matrices & inverse matrices, including Cramer’s rule to solve AX = B

· Performing Gauss-Jordan elimination

· Properties of determinants and how to utilize them to gain insights

· Matrices as vectors, including vector addition and subtraction, Head-to-Tail rule, components, magnitude and midpoint of a vector

· Linear combinations of vectors and span

· Vector spaces, including dimensions, Euclidean spaces, closure properties and axioms

· Subspace and Null-space of a matrix, matrix-vector products

· Spanning set for a vector space and linear dependence

· Basis and standard basis, and checking if a set of given vectors forms the basis for a vector space

· Eigenvalues and Eigenvectors, including how to find Eigenvalues and the corresponding Eigenvectors

· Basic algebra concepts (as a BONUS)

· And so much more…..



HERE IS WHAT YOU GET IN THE COURSE:

Video Lessons:
Watch over my shoulder as I explain all the Linear Algebra concepts in a simple and easy to understand language. Everything is taught from scratch, and no prior knowledge is assumed.

Solved Examples: Every topic is explained with the help of solved examples, from start to end. This problem-based approach is great, especially for beginners who want to practice their Math concepts while learning.

Quizzes: When you think you have understood a concept well, test it by taking the relevant quiz. If you pass, awesome! Otherwise review the suggested lessons and retake the quiz, or ask for help in the Q/A section.

Assignments: Multiple assignments offer you a chance for additional practice by solving sets of relevant and insightful problems (with solutions provided)

By the end of this course, you'll feel confident and comfortable with all the Linear Algebra topics discussed in this course!



WHY SHOULD YOU LEARN LINEAR ALGEBRA?

· Linear Algebra is a prerequisite for many lucrative careers, including Data Science, Artificial Intelligence, Machine Learning, Financial Math, Data Engineering etc.

· Being proficient in Linear Algebra will open doors for you to many high-in-demand careers



WHY LEARN LINEAR ALGEBRA FROM ME?

I took this Linear Algebra class at University of Illinois at Urbana Champaign, one of the Top-5 Engineering Schools in the country, and I have tried to follow the same standards while designing this course.

I have taught various Math and Engineering courses for more than 10 years at schools across US, Asia and Africa. I strongly believe that I have the ability to breakdown complex concepts into easily understandable chunks of information for you!

I provide premium support for all my students - so if you ever get stuck or have a question, just post it to the course dashboard and I'll be there to help you out in a prompt and friendly way!

My goal is to make this the best Linear Algebra and Math course online, and I'll do anything possible to help you learn.



HERE IS WHAT STUDENTS SAY ABOUT THIS COURSE:

I thoroughly enjoyed this course. I needed to get a better understanding and a good base of Linear Algebra for Data Science and Machine Learning and Kashif absolutely delivered. This is definitely a Zero to Hero course on Linear Algebra in my opinion, and would highly recommend this to anyone who is on the same path as I am. Nothing but appreciation for this author. – I. Valderrama

“Wish I had found this earlier” - Dan

“Great explanations. Solid teaching” - J. P. Baugh

“Excellent course! The course material is really good, explanation is really clear and every new concept is provided with examples that make the experience even better! The instructor always takes the time to answer questions poster in Q&A. New material is constantly added to course. Thank you!” – K. Geagea



YOU'LL ALSO GET:

· Lifetime access to “Complete Linear Algebra for Data Science & Machine Learning”

· Friendly support in the Q&A section

· Udemy Certificate of Completion available for download

· 30-day, no-questions-asked, money back guarantee



ENROLL TODAY!

Feel free to check out the course outline below or watch the free preview lessons. Or go ahead and enroll now.

I can’t wait for you to get started with Linear Algebra ?

Cheers,
Kashif


Who this course is for:
  • Students enrolled or planning to enroll in Linear Algebra class, and who want to excel in it
  • Professionals who need a refresher in Math, especially Algebra and Linear Algebra
  • Engineers, Scientists and Mathematicians who want to work with Linear Systems and Vector Spaces
  • Anyone who wants to master Linear Algebra for Data Science, Data Analysis, Artificial Intelligence, Machine Learning, Deep Learning, Computer Graphics, Programming etc.