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.
Linear Algebra for Machine Learning & AI
Linear Algebra for Machine Learning & AI
本课程是 Mathematics for Engineering 专项课程 的一部分
访问权限由 New York State Department of Labor 提供
您将学到什么
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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作业
127 项作业
授课语言：英语（English）
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本课程是 Mathematics for Engineering 专项课程 专项课程的一部分
在注册此课程时，您还会同时注册此专项课程。
- 向行业专家学习新概念
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- 通过实践项目培养工作相关技能
- 获得可共享的职业证书
该课程共有10个模块
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.
涵盖的内容
14个视频5篇阅读材料12个作业
14个视频• 总计101分钟
- Introducing Linear Algebra and Optimization• 3分钟
- Definition of Linear Equations and System of Linear Equations• 9分钟
- Geometric View of a System of Linear Equations with Two Variables• 6分钟
- Matrix Notation • 7分钟
- Matrix Notation and Vector Notation• 5分钟
- Addition of Matrices• 8分钟
- Multiplication of Matrix and a Vector• 8分钟
- Multiplication of Two Matrices• 9分钟
- Transpose of a Matrix• 8分钟
- Introduction to Determinants• 10分钟
- Row Operations of Determinants: Part 1• 9分钟
- Row Operations of Determinants: Part 2• 10分钟
- Det(AB) Equals Det(A).Det(B)• 5分钟
- Wrap-up: Matrices• 3分钟
5篇阅读材料• 总计50分钟
- Course Overview• 10分钟
- Course Structure & Critical Information• 10分钟
- Additional Reading: Linear Equations and System of Linear Equations• 10分钟
- Additional Readings: Matrix Operations• 10分钟
- Additional Readings: Determinants• 10分钟
12个作业• 总计96分钟
- Definition of Linear Equations and System of Linear Equations • 6分钟
- Geometric View of a System of Linear Equations with Two Variables • 9分钟
- Matrix Notation • 9分钟
- Matrix Notation and Vector Notation • 9分钟
- Addition of Matrices • 6分钟
- Multiplication of Matrix and a Vector • 6分钟
- Multiplication of Two Matrices • 9分钟
- Transpose of a Matrix • 9分钟
- Introduction to Determinants • 9分钟
- Row Operations of Determinants• 9分钟
- Row Operations of Determinants• 9分钟
- Det(AB) Equals Det(A).Det(B) • 6分钟
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.
涵盖的内容
14个视频3篇阅读材料14个作业
14个视频• 总计92分钟
- Solving a Linear System by Row Operations (Using Equations)• 9分钟
- Solving a Linear System by Row Operations Using a Matrix• 8分钟
- Existence and Uniqueness Question• 8分钟
- Definition of Echelon Form and Reduced Echelon Form• 8分钟
- Uniqueness of Reduced Echelon Form• 7分钟
- Pivot Position• 4分钟
- Row Reduction Algorithm: Part 1• 8分钟
- Row Reduction Algorithm: Part 2• 6分钟
- Existence and Uniqueness Theorem• 6分钟
- Matrix of Co-factors• 10分钟
- Inverse of a Non-Singular Matrix • 5分钟
- Solving Linear System Using Inverse• 6分钟
- Solving Linear System Using Cramer's Rule• 6分钟
- Wrap-Up: Solution of Linear Systems• 3分钟
3篇阅读材料• 总计30分钟
- Additional Readings: Solving a Linear Systems• 10分钟
- Additional Readings: Row Reduction and Echelon Forms• 10分钟
- Additional Readings: Solving Linear System Using Inverse of a Matrix• 10分钟
14个作业• 总计119分钟
- Solving a Linear System by Row Operations (Using Equations) • 6分钟
- Solving a Linear System by Row Operations Using a Matrix • 9分钟
- Existence and Uniqueness Question • 4分钟
- Definition of Echelon Form and Reduced Echelon Form • 6分钟
- Uniqueness of Reduced Echelon Form • 4分钟
- Pivot Position • 6分钟
- Row Reduction Algorithm• 9分钟
- Row Reduction Algorithm• 6分钟
- Existence and Uniqueness Theorem • 6分钟
- Matrix of Co-factors • 6分钟
- Inverse of a Non-Singular Matrix • 9分钟
- Solving Linear System Using Inverse • 9分钟
- Solving Linear System Using Cramer's Rule • 9分钟
- Test Yourself: Matrices and Linear Systems• 30分钟
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.
涵盖的内容
18个视频5篇阅读材料17个作业
18个视频• 总计139分钟
- Definition of Vector Space• 7分钟
- Examples of Vector Spaces• 10分钟
- Subspace of a Vector Space• 7分钟
- A Subspace Spanned by a Set• 11分钟
- The Null Space of a Matrix• 8分钟
- The Column Space of a Matrix• 9分钟
- The Contrast Between Nul A and Col A• 7分钟
- Definition of a Linear Transformation• 9分钟
- Linear Dependence and Independence• 9分钟
- Definition of Basis• 7分钟
- The Spanning Set Theorem• 9分钟
- Bases for Nul A and Col A • 12分钟
- Dimension of a Vector Space• 9分钟
- The Basis Theorem• 5分钟
- Definition of Row Space• 6分钟
- The Rank Theorem• 8分钟
- The Invertible Matrix Theorem• 4分钟
- Wrap-up: Vector Spaces and Linear Transformations• 3分钟
5篇阅读材料• 总计50分钟
- Additional Readings: Vector Spaces and Subspaces• 10分钟
- Additional Readings: Null Spaces, Column Spaces, and Linear Transformation• 10分钟
- Additional Readings: Linearly Independent Sets • 10分钟
- Additional Readings: Dimension of a Vector Space• 10分钟
- Additional Reading: Rank, Rank Theorem, Invertible Matrix Theorem• 10分钟
17个作业• 总计68分钟
- Vector Space • 6分钟
- Examples of Vector Spaces • 6分钟
- Subspace of a Vector Space • 4分钟
- A Subspace Spanned by a Set • 4分钟
- The Null Space of a Matrix • 4分钟
- The Column Space of a Matrix • 4分钟
- The Contrast Between Nul A and Col A • 4分钟
- Definition of a Linear Transformation • 4分钟
- Linear Dependence and Independence • 6分钟
- Definition of Basis • 4分钟
- The Spanning Set Theorem • 2分钟
- Bases for Nul A and Col A • 4分钟
- Dimension of a Vector Space • 4分钟
- The Basis Theorem • 2分钟
- Definition of Rank • 4分钟
- The Rank Theorem • 4分钟
- The Invertible Matrix Theorem • 2分钟
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.
涵盖的内容
9个视频3篇阅读材料9个作业
9个视频• 总计80分钟
- Definition of Eigenvector and Eigenvalues • 11分钟
- Examples of Eigenvector and Eigenvalues• 10分钟
- Special Cases of Eigenvalues• 9分钟
- The Characteristic Equation• 7分钟
- Examples of Complex Eigenvalues• 11分钟
- Application of Eigenvalues and Eigenvectors• 12分钟
- The Power Method• 9分钟
- Cayley Hamilton Theorem• 7分钟
- Wrap-Up: Eigenvalues and Eigenvectors• 3分钟
3篇阅读材料• 总计30分钟
- Additional Readings: Eigenvalues and Eigenvectors• 10分钟
- Additional Readings: Application of Eigenvalues and Eigenvectors• 10分钟
- Additional Readings: Iterative Estimates of Eigenvalues• 10分钟
9个作业• 总计58分钟
- Practice Quiz: Definition of Eigenvector and Eigenvalues • 4分钟
- Practice Quiz: Examples of Eigenvector and Eigenvalues • 4分钟
- Practice Quiz: Special Cases of Eigenvalues • 2分钟
- Practice Quiz: The Characteristic Equation • 4分钟
- Practice Quiz: Examples of Complex Eigenvalues • 4分钟
- Practice Quiz: Application of Eigenvalues and Eigen Vectors • 2分钟
- Practice Quiz: The Power Method • 4分钟
- Practice Quiz: Cayley Hamilton Theorem • 4分钟
- Test Yourself: Vector Spaces, Linear Transformations, Eigenvalues and Eigenvectors• 30分钟
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.
涵盖的内容
12个视频3篇阅读材料11个作业
12个视频• 总计110分钟
- Gauss Elimination Method• 13分钟
- Examples of Gauss Elimination Method• 12分钟
- Comparison of Gauss-Jordan and Gauss Elimination• 9分钟
- Lower Triangular and Upper Triangular Matrix• 5分钟
- Solving Linear System Using LU Decomposition• 10分钟
- Obtaining LU Decomposition• 15分钟
- Examples on LU Decomposition• 11分钟
- Gauss Jacobi Method• 7分钟
- Examples of Gauss Jacobi Method• 8分钟
- Gauss-Seidel Method• 10分钟
- Examples of Gauss-Seidel Method• 8分钟
- Wrap-up: Numerical Solution of Linear Systems• 2分钟
3篇阅读材料• 总计30分钟
- Gaussian Elimination• 10分钟
- LU Decomposition• 10分钟
- Iterative Methods for Linear Systems• 10分钟
11个作业• 总计38分钟
- Practice Quiz: Gauss Elimination Method • 4分钟
- Practice Quiz: Examples of Gauss Elimination Method • 4分钟
- Practice Quiz: Comparison of Gauss-Jordan and Gauss Elimination • 4分钟
- Practice Quiz: Lower Triangular and Upper Triangular Matrix • 2分钟
- Practice Quiz: Solving Linear System Using LU Decomposition • 2分钟
- Practice Quiz: Obtaining LU Decomposition • 4分钟
- Practice Quiz: Examples on LU Decomposition • 4分钟
- Practice Quiz: Gauss Jacobi Method • 4分钟
- Practice Quiz: Examples of Gauss Jacobi Method • 4分钟
- Practice Quiz: Gauss-Seidel Method • 2分钟
- Practice Quiz: Examples of Gauss-Seidel Method • 4分钟
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.
涵盖的内容
11个视频4篇阅读材料11个作业
11个视频• 总计84分钟
- What is Optimization?• 4分钟
- Optimization Models• 7分钟
- Introduction to LPP• 7分钟
- Concepts of Linear Function and Linear Inequality• 4分钟
- Steps of an LP Formulation • 12分钟
- Basic Assumptions of an LPP• 9分钟
- Linear Programming Applications: Investment• 12分钟
- Linear Programming Applications: Workforce Planning• 10分钟
- Linear Programming Applications: Urban Development Planning• 8分钟
- Linear Programming Applications: Blending• 8分钟
- Wrap-Up: Modeling with Linear Programming• 3分钟
4篇阅读材料• 总计35分钟
- Additional Reading: Introduction to Optimization• 5分钟
- What is Linear Programming Problem (LPP)?• 10分钟
- Formulation of an LPP• 15分钟
- Additional Reading: Linear Programming Applications• 5分钟
11个作业• 总计86分钟
- Practice Quiz: What is Optimization? • 4分钟
- Practice Quiz: Optimization Models • 4分钟
- Practice Quiz: Introduction to LPP • 4分钟
- Practice Quiz: Concepts of Linear Function and Linear Inequality • 4分钟
- Practice Quiz: Steps of an LP Formulation • 30分钟
- Practice Quiz: Basic Assumptions of an LPP • 2分钟
- Practice Quiz: Linear Programming Applications: Investment • 2分钟
- Practice Quiz: Linear Programming Applications: Workforce Planning • 2分钟
- Practice Quiz: Linear Programming Applications: Urban Development Planning • 2分钟
- Practice Quiz: Linear Programming Applications: Blending • 2分钟
- Test Yourself: Linear Systems and Linear Programming• 30分钟
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.
涵盖的内容
16个视频4篇阅读材料15个作业
16个视频• 总计111分钟
- Feasible Solution• 6分钟
- Sketching of Linear Inequalities• 11分钟
- Sketching of Feasible Region• 8分钟
- Determination of the Corner Point of Feasible Region• 7分钟
- Some Basic Definitions• 11分钟
- Definition of Convex Linear Combination• 12分钟
- Definition of Convex Set and Extreme Point• 7分钟
- Few Results on Convex Sets• 4分钟
- Application of an LPP• 5分钟
- Steps in Graphical Solution• 6分钟
- Examples of Graphical Solution of an LPP• 11分钟
- Additional Examples of Graphical Solution of an LPP• 7分钟
- Alternative Optimum Solutions• 7分钟
- Unbounded Solutions• 5分钟
- Infeasible Solutions• 4分钟
- Wrap-up: Graphical Solution and Convex Set• 3分钟
4篇阅读材料• 总计40分钟
- Feasible Region• 10分钟
- Convex Set and LP Theory• 10分钟
- Graphical Solution of LPP • 10分钟
- Special Cases in the Graphical Method• 10分钟
15个作业• 总计72分钟
- Practice Quiz: Feasible Solution • 4分钟
- Practice Quiz: Sketching of Linear Inequalities • 4分钟
- Practice Quiz: Sketching of Feasible Region • 30分钟
- Practice Quiz: Determination of the Corner Point of Feasible Region • 4分钟
- Practice Quiz: Some Basic Definitions • 2分钟
- Practice Quiz: Definition of Convex Linear Combination • 2分钟
- Practice Quiz: Definition of Convex Set and Extreme Point • 4分钟
- Practice Quiz: Few Results on Convex Sets • 2分钟
- Practice Quiz: Application LPP • 2分钟
- Practice Quiz: Steps to Formulate a Graphical Solution • 2分钟
- Practice Quiz: Examples of Graphical Solution • 4分钟
- Practice Quiz: Additional Examples of the Graphical Method • 4分钟
- Practice Quiz: Alternative Optimum Solutions • 2分钟
- Practice Quiz: Unbounded Solutions • 2分钟
- Practice Quiz: Infeasible Solutions • 4分钟
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.
涵盖的内容
15个视频3篇阅读材料14个作业
15个视频• 总计171分钟
- LP Model in Equation Form: Part 1• 10分钟
- LP Model in Equation Form: Part 2• 12分钟
- Basic Solution and Basic Feasible Solution• 10分钟
- Enumeration of All Basic Solutions of an LPP Through an Example• 13分钟
- From Extreme Points to Basic Solutions• 8分钟
- Iterative Nature of the Simplex Method• 10分钟
- The Algebra of the Simplex Method• 16分钟
- Computational Details of the Simplex Method• 15分钟
- Summary of the Simplex Method• 6分钟
- Additional Examples of Solving an LPP Using the Simplex Method• 15分钟
- Generalized Simplex Tableau in a Matrix Form• 12分钟
- Explanation of the Simplex Table in a Matrix Form: Part 1• 9分钟
- Explanation of the Simplex Table in a Matrix Form: Part 2• 14分钟
- Example of a Simplex Table in a Matrix Form• 9分钟
- Wrap-Up: Simplex Method• 12分钟
3篇阅读材料• 总计30分钟
- Transition from Graphical to Algebraic Solution• 10分钟
- The Simplex Method• 10分钟
- Simplex Method Fundamentals• 10分钟
14个作业• 总计78分钟
- Practice Quiz: LP Model in Equation Form • 4分钟
- Practice Quiz: Basic Solution and Basic Feasible Solution • 4分钟
- Practice Quiz: Enumeration of All Basic Solutions of an LPP Through an Example • 4分钟
- Practice Quiz: From Extreme Points to Basic Solutions • 4分钟
- Practice Quiz: Iterative Nature of the Simplex Method • 4分钟
- Practice Quiz: The Algebra of the Simplex Method • 2分钟
- Practice Quiz: Computational Details of the Simplex Method • 4分钟
- Practice Quiz: Summary of the Simplex Method • 4分钟
- Practice Quiz: Additional Examples of Solving an LPP Using the Simplex Method • 4分钟
- Practice Quiz: Generalized Simplex Tableau in a Matrix Form • 4分钟
- Practice Quiz: Explanation of the Simplex Table in a Matrix Form: Part 1 • 2分钟
- Practice Quiz: Explanation of the Simplex Table in a Matrix Form: Part 2 • 4分钟
- Practice Quiz: Example of a Simplex Table in a Matrix Form • 4分钟
- Test Yourself: Solving Linear Programming Problems• 30分钟
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.
涵盖的内容
12个视频3篇阅读材料11个作业
12个视频• 总计108分钟
- Need for Artificial Variable• 9分钟
- Introduction of the M-Method• 8分钟
- Construction of Initial Tableau of the M-Method• 7分钟
- Computational Aspects of the M-Method• 12分钟
- Introduction of the Two-Phase Method• 7分钟
- Computational Aspects of Phase I• 12分钟
- Introduction of Phase II• 8分钟
- Simplex Method: Degeneracy• 9分钟
- Simplex Method: Unbounded Solutions• 6分钟
- Simplex Method: Alternative Optimal Solutions• 16分钟
- Simplex Method: Infeasible Solutions• 8分钟
- Wrap-Up: Artificial Starting Solution and Special Cases in the Simplex Method• 6分钟
3篇阅读材料• 总计25分钟
- Reading: Artificial Variables and the M-Method • 10分钟
- Additional Reading: Artificial Starting Solution• 5分钟
- Special Cases in the Simplex Method• 10分钟
11个作业• 总计26分钟
- Practice Quiz: Need for Artificial Variable • 2分钟
- Practice Quiz: Introduction of the M-Method • 2分钟
- Practice Quiz: Construction of Initial Tableau of the M-Method • 2分钟
- Practice Quiz: Computational Aspects of the M-Method • 4分钟
- Practice Quiz: Introduction of the Two-Phase Method • 2分钟
- Practice Quiz: Computational Aspects of Phase I • 2分钟
- Practice Quiz: Introduction of Phase II • 2分钟
- Practice Quiz: Simplex Method: Degeneracy • 2分钟
- Practice Quiz: Simplex Method: Unbounded Solutions • 2分钟
- Practice Quiz: Simplex Method: Alternative Optimal Solutions • 2分钟
- Practice Quiz: Simplex Method: Infeasible Solutions • 4分钟
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.
涵盖的内容
13个视频3篇阅读材料13个作业
13个视频• 总计104分钟
- Introduction to a Dual Problem Through Example• 7分钟
- Dual Problem: Few Observations• 4分钟
- Example of a Dual Problem Construction• 12分钟
- Finding the Dual in General• 7分钟
- The Fundamental Duality Properties• 12分钟
- How to Find Optimal Solution of Dual• 6分钟
- Example of an Optimal Solution of Dual• 5分钟
- Additional Examples of Duality• 6分钟
- Description of the Dual Simplex Method• 5分钟
- Feasibility Test and Iteration of the Dual Simplex Method• 8分钟
- Solution by Dual Simplex Method: An Example• 14分钟
- Identification of the Infeasible Solution• 10分钟
- Wrap-up: Duality and Dual Simplex Method• 7分钟
3篇阅读材料• 总计30分钟
- Duality• 10分钟
- The Dual Simplex Method• 10分钟
- Course Summary• 10分钟
13个作业• 总计60分钟
- Practice Quiz: Introduction to a Dual Problem Through Example • 4分钟
- Practice Quiz: Dual Problem: Few Observations • 2分钟
- Practice Quiz: Example of a Dual Problem Construction • 2分钟
- Practice Quiz: Finding the Dual in General • 4分钟
- Practice Quiz: The Fundamental Duality Properties • 4分钟
- Practice Quiz: How to Find Optimal Solution of Dual • 2分钟
- Practice Quiz: Example of an Optimal Solution of Dual • 2分钟
- Practice Quiz: Additional Examples of Duality • 2分钟
- Practice Quiz: Description of the Dual Simplex Method • 2分钟
- Practice Quiz: Feasibility Test and Iteration of the Dual Simplex Method • 2分钟
- Practice Quiz: Solution by Dual Simplex Method: An Example • 2分钟
- Practice Quiz: Identification of the Infeasible Solution • 2分钟
- Test Yourself: Artificial Variables, Duality and Dual Simplex Method• 30分钟
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Birla Institute of Technology & Science, Pilani
Birla Institute of Technology & Science, Pilani (BITS Pilani) is one of only ten private universities in India to be recognised as an Institute of Eminence by the Ministry of Human Resource Development, Government of India. It has been consistently ranked high by both governmental and private ranking agencies for its innovative processes and capabilities that have enabled it to impart quality education and emerge as the best private science and engineering institute in India. BITS Pilani has four international campuses in Pilani, Goa, Hyderabad, and Dubai, and has been offering bachelor's, master’s, and certificate programmes for over 58 years, helping to launch the careers for over 1,00,000 professionals.
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