College Level Advanced Linear Algebra! Theory & Programming!
4.5 (279 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.
4,681 students enrolled

College Level Advanced Linear Algebra! Theory & Programming!

Linear Algebra (matlab - python) & Matrix Calculus For Machine Learning, Robotics, Computer Graphics, Control, & more !
4.5 (279 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.
4,681 students enrolled
Created by Ahmed Fathy Hagar
Last updated 10/2019
English
English [Auto], Italian [Auto]
Current price: $139.99 Original price: $199.99 Discount: 30% off
5 hours left at this price!
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This course includes
  • 35 hours on-demand video
  • 15 articles
  • 2 downloadable resources
  • Full lifetime access
  • Access on mobile and TV
  • Certificate of Completion
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What you'll learn
  • Gain Deep Understanding Of Linear Algebra Theoretically, Conceptually & Practically.
  • Obtain A Very Robust Mathematical Foundation For Machine & Deep Learning, Computer Graphics, And Control Systems.
  • Learn How To Use Both Python And Matlab For Solving & Visualizing Linear Algebra Problems.
  • [Matrix Calculus] Learn How To Differentiate & Optimize Complex Equations Involving Matrices.
  • Learn A Lot About Data Science, Co-variance Matrices, And The PCA.
  • Learn About Linear Regression, The Normal Equation, And The Projection Matrix.
  • Learn About Singular Value Decompositions Formally & Conceptually.
  • Learn About Inverses And Pseudo Inverses.
  • Learn About Determinants And Positive Definite Matrices.
  • Learn How To Solve Systems Of Linear, Difference, & Differential Equations Both By Hand And Software.
  • Learn About Lagrange Multipliers & Taylor Expansion.
  • Learn About The Hessian Matrix And Its Importance In Multi-variable Calculus & Optimizations.
  • Learn About Complex Transformation Matrices Like The Matrix To Perform Rotation Around An Arbitrary Axis In 3D.
  • And Much More ! This is a 34+ hours course !
Requirements
  • Be familiar with Linear Algebra basics such as Vectors, Matrices, Dot Products, Cross Products, and Systems Of Linear Equations.
  • For some of the advanced topics presented, I might require you to know some specific topics like partial differentiation or Laplace transform. However, you can easily skip those topics and still completely understand the subsequent sections.
Description

From Matrix Calculus, To Robotics! From Control Systems, To Computer Graphics! From the Singular Value Decompositions to the Principal Component Analysis. From Systems Of Linear Equations, To Systems Of Differential Equations. From Inverses, to Pseudo Inverses. From Determinants, to positive definiteness. From Concepts To Programming. From Matlab To Python. From Proofs to Visualizations & From Theory to Applications. From Solved Examples To thoughtful Exams, and From Many Other Things to Many other things,

I, Present This Course !

My Name is Ahmed Fathy, currently a machine learning scientist at Affectiva,  and a university teacher previously. Over the years, I happened to teach many subjects that make a very deep use of linear algebra. Those include Machine Learning and Deep Learning, Computer Graphics, Control Systems, Game Development, and even Pure Linear Algebra. Every one of those subjects handled linear algebra from very different perspectives. In this course, I provide them all.

This course is intended to be a Reference on linear algebra in the world of online courses, having proofs, theories, programming, concepts, applications, solved examples, visualizations, and everything ! Any suggestions for more topics to add are always welcome. Since the course contents are so large and extensive, I will not summarize them here. Instead, I ask you to please watch the promo video & also have a look on the course contents towards the bottom of the page. Have a nice day !

Who this course is for:
  • Anyone Interested In Linear Algebra, especially, but not limited to, in the context of computer engineering, computer science, or data-science.
  • Anyone Interested In Machine Learning & Deep learning.
  • Anyone Interested In Computer Graphics & Game Development.
  • Anyone Interested In Classical Control Systems & Robotics.
  • Anyone Interested To know how to use python & matlab for Linear Algebra.
  • Anyone Interested In Linear Algebra Theories, Concepts, And Proofs.
Course content
Expand all 296 lectures 35:09:57
+ Introduction To The Course
3 lectures 02:44
Prerequisites
00:49
Exams, Written Scripts & Code Files
00:27
+ Introduction To Matrices : Linear Independence And Matrix Multiplication
11 lectures 01:18:51
Linear Combinations And Independence - 1
10:43
Linear Combinations And Independence - 2
07:03
The Planes Picture vs The Vectors Picture
22:43
Matrix Rank And Case Of Rectangular Matrices
12:52
Row By Matrix Multiplication
05:30
Matrix Matrix Multiplication - 1 - Dot Product Method
01:20
Matrix Matrix Multiplication - 2 - Column Method
02:10
Matrix Matrix Multiplication - 3 - Row Method
01:42
Matrix Matrix Multiplication - 4 - Outer Product
03:44
Matrix Matrix Multiplication - 5 - Block Multiplication
05:45
+ Introduction To Gaussian Elimination And Matrix Inverse
9 lectures 56:20
Introduction To Gaussian Elimination
11:03
Gaussian Elimination With Row Exchange
07:03
Elimination Using Matrices
05:05
Row And Column Exchange Using Matrices
04:38
Intuition Of Matrix Inverse
05:02
Python Example & Matrix Inverse by Intuition
06:51
Gauss-Jordan Inverse with proof
02:53
Python, Matlab & Hand Example For Matrix Inverse
06:02
Notes Regarding Inverses, Determinants, And Pseudo-Inverses
07:43
+ Test Your Self ! - Exam 1 !
1 lecture 00:13
Test Your Self ! - Exam 1 !
00:13
+ The Computer Graphics Section !
21 lectures 02:55:29
Introduction To Computer Graphics
06:15
The Computer Graphics Pipeline
10:39
Rotation By 90 Degrees Matrix in 2D
05:34
Rotation By Arbitrary Angle Matrix In 2D
07:38
Orthogonal Matrices And Their Inverses
02:39
Rotation About The X-Axis in 3D
02:34
The Scaling Matrix
02:01
The Homogeneous Coordinates And Translation Matrices
06:27
The Order Of Transformation Matters !
14:11
Reflection Matrix Around The X-Axis
03:14
Reflection Around Arbitrary Line in 2D - Method I
11:54
Reflection Around Arbitrary Line In 2D - Method II
06:31
Rotation About Arbitrary Axis in 3D - Method I
12:46
Rotation About Arbitrary Axis In 3D - Method II
12:16
Reflection Around Arbitrary Plane In 3D
07:18
Rotations & Improper Rotations
15:54
Notes About The Following Three Videos
00:13
Mathematics Of The Camera - I
07:23
Mathematics Of The Camera - II
10:07
Mathematics Of The Camera - III
14:11
Hierarchical Transformations And The Scene Graph
15:44
+ The Robotics Section !
6 lectures 45:47
Robotics And Change Of Reference Frames - I
04:13
Robotics And Change Of Reference Frames II
06:09
Robotics And Change Of Reference Frames III
11:07
Matlab : Robotics And Change Of Reference Frames IV - Numerical Example in 2D
11:00
Robotics And Change Of Reference Frames V - The 3D situation
08:07
Robotics And Change Of Reference Frames VI - The Camera Matrix Revisited
05:11
+ Test Your Self ! - Exam 2 !
1 lecture 00:13
Test Your Self ! - Exam 2 !
00:13
+ Test Your Self ! - Exam 3 !
1 lecture 00:13
Test Your Self ! - Exam 3 !
00:13
+ EigenValues & EigenVectors ( I ) : Introduction
14 lectures 01:12:40
Introduction To EigenValues And EigenVectors
01:01
EigenVs Geomteric Definition
04:50
EigenVs - Intuitive Examples I
07:24
EigenVs Intuitive Examples II
04:33
EigenVs Formal Calculation
04:27
EigenVs Numerical Examples - I
08:11
EigenVs Numerical Examples - II
06:04
Repeated EigenValues And Dependent EigenVectors
03:54
The Rotation Matrix And Complex EigenVectors
03:31
Proof : Different EigenValues have Independent EigenVectors
09:00
Matrix Diagonalization Using Eigen Decomposition
06:25
Complex EigenVs For Real Matrices Are Always Conjugate Pairs
06:00
Matrix Powers & Eigen Decomposition
03:04
Determinant Is The Product Of EigenValues
04:16
+ EigenValues & EigenVectors ( II ) : Difference Equations
5 lectures 43:19
Difference Equations & Eigen Decomposition
09:49
Matlab : Visualization Of Difference Equations Solved Example
07:33
Transforming Recurrence Relations To Matrix Form
09:01
The Case Of Complex EigenVs & Difference Equations
11:27
Matlab : Visualization Of Complex EigenVs And Difference Equations
05:29