Linear Algebra for Machine Learning & AI
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Linear Algebra for Machine Learning & AI
This course is part of Mathematics for Engineering Specialization
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What you'll learn
Analyse and evaluate complex data structures using advanced linear algebra techniques.
Implement sophisticated algorithms and apply advanced techniques to optimise and improve machine learning models.
Synthesise and apply mathematical theories to solve complex real-world problems.
Evaluate and develop innovative solutions using linear programming to address complex challenges in machine learning and AI systems.
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There are 10 modules in this course
Unlock the powerful world of Machine Learning and Artificial Intelligence with our comprehensive, hands-on course on Linear Algebra. This course serves as an essential stepping stone for aspiring data scientists, AI practitioners, software developers, and tech enthusiasts eager to build a solid mathematical foundation for these high-demand fields.
Designed for individuals pursuing a career in tech or enhancing skills in data analysis and AI development, this course bridges theoretical mathematics with practical AI applications. Dive into key concepts such as matrices, linear systems, eigenvalues, linear transformations, and linear programming. Through practical exercises, interactive discussions, and real-world applications, you'll develop analytical skills and systematic problem-solving capabilities crucial for optimizing models and analyzing data. Ideal for professionals aiming to up skill for roles in machine learning engineering, AI research, data science, and software development, this course empowers you to advance your career and become an essential contributor to the tech industry. Master the mathematical secrets behind AI and Machine Learning to enhance your career prospects and stay ahead in the digital age. Enrol today and transform your understanding of linear algebra into a valuable asset for the future.
In this module, you will be introduced to linear system of equations and matrices. You will also learn about the properties of matrices and operations like addition and multiplication. Finally, the module also discusses determinants and its elementary properties.
What's included
14 videos5 readings12 assignments
14 videos•Total 101 minutes
- Introducing Linear Algebra and Optimization•3 minutes
- Definition of Linear Equations and System of Linear Equations•9 minutes
- Geometric View of a System of Linear Equations with Two Variables•6 minutes
- Matrix Notation •7 minutes
- Matrix Notation and Vector Notation•5 minutes
- Addition of Matrices•8 minutes
- Multiplication of Matrix and a Vector•8 minutes
- Multiplication of Two Matrices•9 minutes
- Transpose of a Matrix•8 minutes
- Introduction to Determinants•10 minutes
- Row Operations of Determinants: Part 1•9 minutes
- Row Operations of Determinants: Part 2•10 minutes
- Det(AB) Equals Det(A).Det(B)•5 minutes
- Wrap-up: Matrices•3 minutes
5 readings•Total 50 minutes
- Course Overview•10 minutes
- Course Structure & Critical Information•10 minutes
- Additional Reading: Linear Equations and System of Linear Equations•10 minutes
- Additional Readings: Matrix Operations•10 minutes
- Additional Readings: Determinants•10 minutes
12 assignments•Total 96 minutes
- Definition of Linear Equations and System of Linear Equations •6 minutes
- Geometric View of a System of Linear Equations with Two Variables •9 minutes
- Matrix Notation •9 minutes
- Matrix Notation and Vector Notation •9 minutes
- Addition of Matrices •6 minutes
- Multiplication of Matrix and a Vector •6 minutes
- Multiplication of Two Matrices •9 minutes
- Transpose of a Matrix •9 minutes
- Introduction to Determinants •9 minutes
- Row Operations of Determinants•9 minutes
- Row Operations of Determinants•9 minutes
- Det(AB) Equals Det(A).Det(B) •6 minutes
In this module, you will learn how to solve a system of linear equations and describe their nature of solutions. You will define the criteria to determine the consistency of linear systems, a concept that would help you determine the nature of solutions. Lastly, you will also gain insight into analytical methods such as the Gauss elimination method, matrix inversion method, and Cramer’s rule.
What's included
14 videos3 readings14 assignments
14 videos•Total 92 minutes
- Solving a Linear System by Row Operations (Using Equations)•9 minutes
- Solving a Linear System by Row Operations Using a Matrix•8 minutes
- Existence and Uniqueness Question•8 minutes
- Definition of Echelon Form and Reduced Echelon Form•8 minutes
- Uniqueness of Reduced Echelon Form•7 minutes
- Pivot Position•4 minutes
- Row Reduction Algorithm: Part 1•8 minutes
- Row Reduction Algorithm: Part 2•6 minutes
- Existence and Uniqueness Theorem•6 minutes
- Matrix of Co-factors•10 minutes
- Inverse of a Non-Singular Matrix •5 minutes
- Solving Linear System Using Inverse•6 minutes
- Solving Linear System Using Cramer's Rule•6 minutes
- Wrap-Up: Solution of Linear Systems•3 minutes
3 readings•Total 30 minutes
- Additional Readings: Solving a Linear Systems•10 minutes
- Additional Readings: Row Reduction and Echelon Forms•10 minutes
- Additional Readings: Solving Linear System Using Inverse of a Matrix•10 minutes
14 assignments•Total 119 minutes
- Test Yourself: Matrices and Linear Systems•30 minutes
- Solving a Linear System by Row Operations (Using Equations) •6 minutes
- Solving a Linear System by Row Operations Using a Matrix •9 minutes
- Existence and Uniqueness Question •4 minutes
- Definition of Echelon Form and Reduced Echelon Form •6 minutes
- Uniqueness of Reduced Echelon Form •4 minutes
- Pivot Position •6 minutes
- Row Reduction Algorithm•9 minutes
- Row Reduction Algorithm•6 minutes
- Existence and Uniqueness Theorem •6 minutes
- Matrix of Co-factors •6 minutes
- Inverse of a Non-Singular Matrix •9 minutes
- Solving Linear System Using Inverse •9 minutes
- Solving Linear System Using Cramer's Rule •9 minutes
In this module, you will learn about vector spaces. The concepts required to characterise vector spaces, such as linear dependence, linear independence, linear span, basis, and dimension will be discussed in detail. You will also learn linear transformation and its properties, including the rank–nullity theorem.
What's included
18 videos5 readings17 assignments
18 videos•Total 139 minutes
- Definition of Vector Space•7 minutes
- Examples of Vector Spaces•10 minutes
- Subspace of a Vector Space•7 minutes
- A Subspace Spanned by a Set•11 minutes
- The Null Space of a Matrix•8 minutes
- The Column Space of a Matrix•9 minutes
- The Contrast Between Nul A and Col A•7 minutes
- Definition of a Linear Transformation•9 minutes
- Linear Dependence and Independence•9 minutes
- Definition of Basis•7 minutes
- The Spanning Set Theorem•9 minutes
- Bases for Nul A and Col A •12 minutes
- Dimension of a Vector Space•9 minutes
- The Basis Theorem•5 minutes
- Definition of Row Space•6 minutes
- The Rank Theorem•8 minutes
- The Invertible Matrix Theorem•4 minutes
- Wrap-up: Vector Spaces and Linear Transformations•3 minutes
5 readings•Total 50 minutes
- Additional Readings: Vector Spaces and Subspaces•10 minutes
- Additional Readings: Null Spaces, Column Spaces, and Linear Transformation•10 minutes
- Additional Readings: Linearly Independent Sets •10 minutes
- Additional Readings: Dimension of a Vector Space•10 minutes
- Additional Reading: Rank, Rank Theorem, Invertible Matrix Theorem•10 minutes
17 assignments•Total 68 minutes
- Vector Space •6 minutes
- Examples of Vector Spaces •6 minutes
- Subspace of a Vector Space •4 minutes
- A Subspace Spanned by a Set •4 minutes
- The Null Space of a Matrix •4 minutes
- The Column Space of a Matrix •4 minutes
- The Contrast Between Nul A and Col A •4 minutes
- Definition of a Linear Transformation •4 minutes
- Linear Dependence and Independence •6 minutes
- Definition of Basis •4 minutes
- The Spanning Set Theorem •2 minutes
- Bases for Nul A and Col A •4 minutes
- Dimension of a Vector Space •4 minutes
- The Basis Theorem •2 minutes
- Definition of Rank •4 minutes
- The Rank Theorem •4 minutes
- The Invertible Matrix Theorem •2 minutes
In this module, you will learn how to determine eigenvalues and the corresponding eigenvectors of square matrices. Certain properties of eigenvalues and eigenvectors pertaining to special matrices would be explained in detail after introducing the necessary concepts on complex numbers. You will also gain insight into computing eigenvalues numerically using the Power method.
What's included
9 videos3 readings9 assignments
9 videos•Total 80 minutes
- Definition of Eigenvector and Eigenvalues •11 minutes
- Examples of Eigenvector and Eigenvalues•10 minutes
- Special Cases of Eigenvalues•9 minutes
- The Characteristic Equation•7 minutes
- Examples of Complex Eigenvalues•11 minutes
- Application of Eigenvalues and Eigenvectors•12 minutes
- The Power Method•9 minutes
- Cayley Hamilton Theorem•7 minutes
- Wrap-Up: Eigenvalues and Eigenvectors•3 minutes
3 readings•Total 30 minutes
- Additional Readings: Eigenvalues and Eigenvectors•10 minutes
- Additional Readings: Application of Eigenvalues and Eigenvectors•10 minutes
- Additional Readings: Iterative Estimates of Eigenvalues•10 minutes
9 assignments•Total 58 minutes
- Test Yourself: Vector Spaces, Linear Transformations, Eigenvalues and Eigenvectors•30 minutes
- Practice Quiz: Definition of Eigenvector and Eigenvalues •4 minutes
- Practice Quiz: Examples of Eigenvector and Eigenvalues •4 minutes
- Practice Quiz: Special Cases of Eigenvalues •2 minutes
- Practice Quiz: The Characteristic Equation •4 minutes
- Practice Quiz: Examples of Complex Eigenvalues •4 minutes
- Practice Quiz: Application of Eigenvalues and Eigen Vectors •2 minutes
- Practice Quiz: The Power Method •4 minutes
- Practice Quiz: Cayley Hamilton Theorem •4 minutes
In this module, you will explore the methods of solving a linear system numerically. You will also learn methods such as decomposition methods and iterative methods, namely Gauss–Seidel and Jacobi methods, to compute solutions of linear systems.
What's included
12 videos3 readings11 assignments
12 videos•Total 110 minutes
- Gauss Elimination Method•13 minutes
- Examples of Gauss Elimination Method•12 minutes
- Comparison of Gauss-Jordan and Gauss Elimination•9 minutes
- Lower Triangular and Upper Triangular Matrix•5 minutes
- Solving Linear System Using LU Decomposition•10 minutes
- Obtaining LU Decomposition•15 minutes
- Examples on LU Decomposition•11 minutes
- Gauss Jacobi Method•7 minutes
- Examples of Gauss Jacobi Method•8 minutes
- Gauss-Seidel Method•10 minutes
- Examples of Gauss-Seidel Method•8 minutes
- Wrap-up: Numerical Solution of Linear Systems•2 minutes
3 readings•Total 30 minutes
- Gaussian Elimination•10 minutes
- LU Decomposition•10 minutes
- Iterative Methods for Linear Systems•10 minutes
11 assignments•Total 38 minutes
- Practice Quiz: Gauss Elimination Method •4 minutes
- Practice Quiz: Examples of Gauss Elimination Method •4 minutes
- Practice Quiz: Comparison of Gauss-Jordan and Gauss Elimination •4 minutes
- Practice Quiz: Lower Triangular and Upper Triangular Matrix •2 minutes
- Practice Quiz: Solving Linear System Using LU Decomposition •2 minutes
- Practice Quiz: Obtaining LU Decomposition •4 minutes
- Practice Quiz: Examples on LU Decomposition •4 minutes
- Practice Quiz: Gauss Jacobi Method •4 minutes
- Practice Quiz: Examples of Gauss Jacobi Method •4 minutes
- Practice Quiz: Gauss-Seidel Method •2 minutes
- Practice Quiz: Examples of Gauss-Seidel Method •4 minutes
In this module, you will learn about the formulation of Linear Programming Problems (LPP) using practical applications. You will also gain insight into the concepts of objective function and constraints.
What's included
11 videos4 readings11 assignments
11 videos•Total 84 minutes
- What is Optimization?•4 minutes
- Optimization Models•7 minutes
- Introduction to LPP•7 minutes
- Concepts of Linear Function and Linear Inequality•4 minutes
- Steps of an LP Formulation •12 minutes
- Basic Assumptions of an LPP•9 minutes
- Linear Programming Applications: Investment•12 minutes
- Linear Programming Applications: Workforce Planning•10 minutes
- Linear Programming Applications: Urban Development Planning•8 minutes
- Linear Programming Applications: Blending•8 minutes
- Wrap-Up: Modeling with Linear Programming•3 minutes
4 readings•Total 35 minutes
- Additional Reading: Introduction to Optimization•5 minutes
- What is Linear Programming Problem (LPP)?•10 minutes
- Formulation of an LPP•15 minutes
- Additional Reading: Linear Programming Applications•5 minutes
11 assignments•Total 86 minutes
- Test Yourself: Linear Systems and Linear Programming•30 minutes
- Practice Quiz: What is Optimization? •4 minutes
- Practice Quiz: Optimization Models •4 minutes
- Practice Quiz: Introduction to LPP •4 minutes
- Practice Quiz: Concepts of Linear Function and Linear Inequality •4 minutes
- Practice Quiz: Steps of an LP Formulation •30 minutes
- Practice Quiz: Basic Assumptions of an LPP •2 minutes
- Practice Quiz: Linear Programming Applications: Investment •2 minutes
- Practice Quiz: Linear Programming Applications: Workforce Planning •2 minutes
- Practice Quiz: Linear Programming Applications: Urban Development Planning •2 minutes
- Practice Quiz: Linear Programming Applications: Blending •2 minutes
In this module, you will learn about the graphical solution of linear programming problems with two decision variables and the basic concepts of convex sets and application to Linear Programming Problems.
What's included
16 videos4 readings15 assignments
16 videos•Total 111 minutes
- Feasible Solution•6 minutes
- Sketching of Linear Inequalities•11 minutes
- Sketching of Feasible Region•8 minutes
- Determination of the Corner Point of Feasible Region•7 minutes
- Some Basic Definitions•11 minutes
- Definition of Convex Linear Combination•12 minutes
- Definition of Convex Set and Extreme Point•7 minutes
- Few Results on Convex Sets•4 minutes
- Application of an LPP•5 minutes
- Steps in Graphical Solution•6 minutes
- Examples of Graphical Solution of an LPP•11 minutes
- Additional Examples of Graphical Solution of an LPP•7 minutes
- Alternative Optimum Solutions•7 minutes
- Unbounded Solutions•5 minutes
- Infeasible Solutions•4 minutes
- Wrap-up: Graphical Solution and Convex Set•3 minutes
4 readings•Total 40 minutes
- Feasible Region•10 minutes
- Convex Set and LP Theory•10 minutes
- Graphical Solution of LPP •10 minutes
- Special Cases in the Graphical Method•10 minutes
15 assignments•Total 72 minutes
- Practice Quiz: Feasible Solution •4 minutes
- Practice Quiz: Sketching of Linear Inequalities •4 minutes
- Practice Quiz: Sketching of Feasible Region •30 minutes
- Practice Quiz: Determination of the Corner Point of Feasible Region •4 minutes
- Practice Quiz: Some Basic Definitions •2 minutes
- Practice Quiz: Definition of Convex Linear Combination •2 minutes
- Practice Quiz: Definition of Convex Set and Extreme Point •4 minutes
- Practice Quiz: Few Results on Convex Sets •2 minutes
- Practice Quiz: Application LPP •2 minutes
- Practice Quiz: Steps to Formulate a Graphical Solution •2 minutes
- Practice Quiz: Examples of Graphical Solution •4 minutes
- Practice Quiz: Additional Examples of the Graphical Method •4 minutes
- Practice Quiz: Alternative Optimum Solutions •2 minutes
- Practice Quiz: Unbounded Solutions •2 minutes
- Practice Quiz: Infeasible Solutions •4 minutes
In this module, you will learn to solve an LPP algebraically by using a procedure called the simplex method. You will also be introduced to the concepts of slack and surplus variables, basic solution, and basic feasible solution. Lastly, you will learn to construct Simplex Tableau using matrix manipulation.
What's included
15 videos3 readings14 assignments
15 videos•Total 171 minutes
- LP Model in Equation Form: Part 1•10 minutes
- LP Model in Equation Form: Part 2•12 minutes
- Basic Solution and Basic Feasible Solution•10 minutes
- Enumeration of All Basic Solutions of an LPP Through an Example•13 minutes
- From Extreme Points to Basic Solutions•8 minutes
- Iterative Nature of the Simplex Method•10 minutes
- The Algebra of the Simplex Method•16 minutes
- Computational Details of the Simplex Method•15 minutes
- Summary of the Simplex Method•6 minutes
- Additional Examples of Solving an LPP Using the Simplex Method•15 minutes
- Generalized Simplex Tableau in a Matrix Form•12 minutes
- Explanation of the Simplex Table in a Matrix Form: Part 1•9 minutes
- Explanation of the Simplex Table in a Matrix Form: Part 2•14 minutes
- Example of a Simplex Table in a Matrix Form•9 minutes
- Wrap-Up: Simplex Method•12 minutes
3 readings•Total 30 minutes
- Transition from Graphical to Algebraic Solution•10 minutes
- The Simplex Method•10 minutes
- Simplex Method Fundamentals•10 minutes
14 assignments•Total 78 minutes
- Test Yourself: Solving Linear Programming Problems•30 minutes
- Practice Quiz: LP Model in Equation Form •4 minutes
- Practice Quiz: Basic Solution and Basic Feasible Solution •4 minutes
- Practice Quiz: Enumeration of All Basic Solutions of an LPP Through an Example •4 minutes
- Practice Quiz: From Extreme Points to Basic Solutions •4 minutes
- Practice Quiz: Iterative Nature of the Simplex Method •4 minutes
- Practice Quiz: The Algebra of the Simplex Method •2 minutes
- Practice Quiz: Computational Details of the Simplex Method •4 minutes
- Practice Quiz: Summary of the Simplex Method •4 minutes
- Practice Quiz: Additional Examples of Solving an LPP Using the Simplex Method •4 minutes
- Practice Quiz: Generalized Simplex Tableau in a Matrix Form •4 minutes
- Practice Quiz: Explanation of the Simplex Table in a Matrix Form: Part 1 •2 minutes
- Practice Quiz: Explanation of the Simplex Table in a Matrix Form: Part 2 •4 minutes
- Practice Quiz: Example of a Simplex Table in a Matrix Form •4 minutes
In this module, you will learn the concept of artificial variables. You will also learn M-method and Two-Phase method for solving LPP. You will recognize various special cases such as unboundedness, infeasibility, and alternate optima.
What's included
12 videos3 readings11 assignments
12 videos•Total 108 minutes
- Need for Artificial Variable•9 minutes
- Introduction of the M-Method•8 minutes
- Construction of Initial Tableau of the M-Method•7 minutes
- Computational Aspects of the M-Method•12 minutes
- Introduction of the Two-Phase Method•7 minutes
- Computational Aspects of Phase I•12 minutes
- Introduction of Phase II•8 minutes
- Simplex Method: Degeneracy•9 minutes
- Simplex Method: Unbounded Solutions•6 minutes
- Simplex Method: Alternative Optimal Solutions•16 minutes
- Simplex Method: Infeasible Solutions•8 minutes
- Wrap-Up: Artificial Starting Solution and Special Cases in the Simplex Method•6 minutes
3 readings•Total 25 minutes
- Reading: Artificial Variables and the M-Method •10 minutes
- Additional Reading: Artificial Starting Solution•5 minutes
- Special Cases in the Simplex Method•10 minutes
11 assignments•Total 26 minutes
- Practice Quiz: Need for Artificial Variable •2 minutes
- Practice Quiz: Introduction of the M-Method •2 minutes
- Practice Quiz: Construction of Initial Tableau of the M-Method •2 minutes
- Practice Quiz: Computational Aspects of the M-Method •4 minutes
- Practice Quiz: Introduction of the Two-Phase Method •2 minutes
- Practice Quiz: Computational Aspects of Phase I •2 minutes
- Practice Quiz: Introduction of Phase II •2 minutes
- Practice Quiz: Simplex Method: Degeneracy •2 minutes
- Practice Quiz: Simplex Method: Unbounded Solutions •2 minutes
- Practice Quiz: Simplex Method: Alternative Optimal Solutions •2 minutes
- Practice Quiz: Simplex Method: Infeasible Solutions •4 minutes
In this module, you will learn the construction of a dual problem and the relationship between primal and dual. You will also learn the procedure of the dual simplex method.
What's included
13 videos3 readings13 assignments
13 videos•Total 104 minutes
- Introduction to a Dual Problem Through Example•7 minutes
- Dual Problem: Few Observations•4 minutes
- Example of a Dual Problem Construction•12 minutes
- Finding the Dual in General•7 minutes
- The Fundamental Duality Properties•12 minutes
- How to Find Optimal Solution of Dual•6 minutes
- Example of an Optimal Solution of Dual•5 minutes
- Additional Examples of Duality•6 minutes
- Description of the Dual Simplex Method•5 minutes
- Feasibility Test and Iteration of the Dual Simplex Method•8 minutes
- Solution by Dual Simplex Method: An Example•14 minutes
- Identification of the Infeasible Solution•10 minutes
- Wrap-up: Duality and Dual Simplex Method•7 minutes
3 readings•Total 30 minutes
- Duality•10 minutes
- The Dual Simplex Method•10 minutes
- Course Summary•10 minutes
13 assignments•Total 60 minutes
- Test Yourself: Artificial Variables, Duality and Dual Simplex Method•30 minutes
- Practice Quiz: Introduction to a Dual Problem Through Example •4 minutes
- Practice Quiz: Dual Problem: Few Observations •2 minutes
- Practice Quiz: Example of a Dual Problem Construction •2 minutes
- Practice Quiz: Finding the Dual in General •4 minutes
- Practice Quiz: The Fundamental Duality Properties •4 minutes
- Practice Quiz: How to Find Optimal Solution of Dual •2 minutes
- Practice Quiz: Example of an Optimal Solution of Dual •2 minutes
- Practice Quiz: Additional Examples of Duality •2 minutes
- Practice Quiz: Description of the Dual Simplex Method •2 minutes
- Practice Quiz: Feasibility Test and Iteration of the Dual Simplex Method •2 minutes
- Practice Quiz: Solution by Dual Simplex Method: An Example •2 minutes
- Practice Quiz: Identification of the Infeasible Solution •2 minutes
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This course is part of the following degree program(s) offered by Birla Institute of Technology & Science, Pilani. If you are admitted and enroll, your completed coursework may count toward your degree learning and your progress can transfer with you.¹
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