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Linear Algebra for Machine Learning & AI · LearnSpace
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Linear Algebra for Machine Learning & AI

Курс от Birla Institute of Technology & Science, Pilani
Начальный≈ 36.9 чАнглийский
О курсеНавыкиПрограммаПреподаватели

О курсе

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.

Навыки, которые вы освоите

Linear AlgebraModel OptimizationNumerical AnalysisData AnalysisArtificial Intelligence and Machine Learning (AI/ML)Machine LearningArtificial Neural NetworksDimensionality ReductionApplied Mathematics

Программа курса

10 модулей · 301 учебных материалов

01Matrices32 материалов

Let's Get Started

Introducing Linear Algebra and OptimizationВидеоCourse OverviewЧтениеCourse Structure & Critical InformationЧтение

System of Linear Equations

Definition of Linear Equations and System of Linear EquationsВидео

Учитесь у экспертов

BITS Pilani Instructors Group

Преподаватель курса

Linear Algebra for Machine Learning & AI
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Обучение откроется на Coursera
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Обучение на Coursera

≈ 36.9 ч

10 модулей

Язык: Английский

Субтитры: Венгерский

Часть программы вашего университета
Definition of Linear Equations and System of Linear Equations Задание
Geometric View of a System of Linear Equations with Two VariablesВидео
Geometric View of a System of Linear Equations with Two Variables Задание
Matrix Notation Видео
Matrix Notation Задание
Matrix Notation and Vector NotationВидео
Matrix Notation and Vector Notation Задание
Additional Reading: Linear Equations and System of Linear EquationsЧтение

Matrix Operations

Addition of MatricesВидеоAddition of Matrices ЗаданиеMultiplication of Matrix and a VectorВидеоMultiplication of Matrix and a Vector ЗаданиеMultiplication of Two MatricesВидеоMultiplication of Two Matrices ЗаданиеTranspose of a MatrixВидеоTranspose of a Matrix ЗаданиеAdditional Readings: Matrix OperationsЧтение

Determinants

Introduction to DeterminantsВидеоIntroduction to Determinants ЗаданиеRow Operations of Determinants: Part 1ВидеоRow Operations of DeterminantsЗаданиеRow Operations of Determinants: Part 2ВидеоRow Operations of DeterminantsЗаданиеDet(AB) Equals Det(A).Det(B)ВидеоDet(AB) Equals Det(A).Det(B) ЗаданиеAdditional Readings: DeterminantsЧтениеMatrix Operations in Real-World ApplicationsDIALOGUE

Summary

Wrap-up: MatricesВидео
02Solving Linear Systems31 материалов

Introduction to Solving a Linear Systems

Solving a Linear System by Row Operations (Using Equations)ВидеоSolving a Linear System by Row Operations (Using Equations) ЗаданиеSolving a Linear System by Row Operations Using a MatrixВидеоSolving a Linear System by Row Operations Using a Matrix ЗаданиеExistence and Uniqueness QuestionВидеоExistence and Uniqueness Question ЗаданиеAdditional Readings: Solving a Linear SystemsЧтение

Row Reduction and Echelon Forms

Definition of Echelon Form and Reduced Echelon FormВидеоDefinition of Echelon Form and Reduced Echelon Form ЗаданиеUniqueness of Reduced Echelon FormВидеоUniqueness of Reduced Echelon Form ЗаданиеPivot PositionВидеоPivot Position Задание

Solving Linear System Using Inverse of a Matrix

Matrix of Co-factorsВидеоMatrix of Co-factors ЗаданиеInverse of a Non-Singular Matrix ВидеоInverse of a Non-Singular Matrix ЗаданиеSolving Linear System Using InverseВидеоSolving Linear System Using Inverse Задание

Summary and Assessment

Wrap-Up: Solution of Linear SystemsВидеоTest Yourself: Matrices and Linear SystemsЗадание
03Vector Spaces and Linear Transformations41 материалов

Vector Spaces and Subspaces

Definition of Vector SpaceВидеоVector Space ЗаданиеExamples of Vector SpacesВидеоExamples of Vector Spaces ЗаданиеSubspace of a Vector SpaceВидеоSubspace of a Vector Space ЗаданиеA Subspace Spanned by a SetВидеоA Subspace Spanned by a Set ЗаданиеAdditional Readings: Vector Spaces and SubspacesЧтение

Null Spaces, Column Spaces, and Linear Transformation

The Null Space of a MatrixВидеоThe Null Space of a Matrix ЗаданиеThe Column Space of a MatrixВидеоThe Column Space of a Matrix ЗаданиеThe Contrast Between Nul A and Col AВидеоThe Contrast Between Nul A and Col A Задание

Linearly Independent Sets

Linear Dependence and IndependenceВидеоLinear Dependence and Independence ЗаданиеDefinition of BasisВидеоDefinition of Basis ЗаданиеThe Spanning Set TheoremВидеоThe Spanning Set Theorem ЗаданиеBases for Nul A and Col A

Dimension of a Vector Space

Dimension of a Vector SpaceВидеоDimension of a Vector Space ЗаданиеThe Basis TheoremВидеоThe Basis Theorem ЗаданиеAdditional Readings: Dimension of a Vector SpaceЧтение

Rank

Definition of Row SpaceВидеоDefinition of Rank ЗаданиеThe Rank TheoremВидеоThe Rank Theorem ЗаданиеThe Invertible Matrix TheoremВидеоThe Invertible Matrix Theorem ЗаданиеAdditional Reading: Rank, Rank Theorem, Invertible Matrix Theorem

Summary

Wrap-up: Vector Spaces and Linear TransformationsВидео
04Eigenvalues and Eigenvectors21 материалов

Eigenvalues and Eigenvectors

Definition of Eigenvector and Eigenvalues ВидеоPractice Quiz: Definition of Eigenvector and Eigenvalues ЗаданиеExamples of Eigenvector and EigenvaluesВидеоPractice Quiz: Examples of Eigenvector and Eigenvalues ЗаданиеSpecial Cases of EigenvaluesВидеоPractice Quiz: Special Cases of Eigenvalues ЗаданиеThe Characteristic EquationВидеоPractice Quiz: The Characteristic Equation ЗаданиеAdditional Readings: Eigenvalues and EigenvectorsЧтение

Application of Eigenvalues and Eigenvectors

Examples of Complex EigenvaluesВидеоPractice Quiz: Examples of Complex Eigenvalues ЗаданиеApplication of Eigenvalues and EigenvectorsВидеоPractice Quiz: Application of Eigenvalues and Eigen Vectors ЗаданиеAdditional Readings: Application of Eigenvalues and EigenvectorsЧтение

Iterative Estimates of Eigenvalues

The Power MethodВидеоPractice Quiz: The Power Method ЗаданиеCayley Hamilton TheoremВидеоPractice Quiz: Cayley Hamilton Theorem ЗаданиеAdditional Readings: Iterative Estimates of EigenvaluesЧтение

Summary and Assessment

Wrap-Up: Eigenvalues and EigenvectorsВидеоTest Yourself: Vector Spaces, Linear Transformations, Eigenvalues and EigenvectorsЗадание
05Numerical Solution of Linear Systems27 материалов

Gaussian Elimination

Gauss Elimination MethodВидеоPractice Quiz: Gauss Elimination Method ЗаданиеExamples of Gauss Elimination MethodВидеоPractice Quiz: Examples of Gauss Elimination Method ЗаданиеComparison of Gauss-Jordan and Gauss EliminationВидеоPractice Quiz: Comparison of Gauss-Jordan and Gauss Elimination ЗаданиеGaussian EliminationЧтение

LU Decomposition

Lower Triangular and Upper Triangular MatrixВидеоPractice Quiz: Lower Triangular and Upper Triangular Matrix ЗаданиеSolving Linear System Using LU DecompositionВидеоPractice Quiz: Solving Linear System Using LU Decomposition ЗаданиеObtaining LU DecompositionВидеоPractice Quiz: Obtaining LU Decomposition Задание

Iterative Methods for Linear Systems

Gauss Jacobi MethodВидеоPractice Quiz: Gauss Jacobi Method ЗаданиеExamples of Gauss Jacobi MethodВидеоPractice Quiz: Examples of Gauss Jacobi Method ЗаданиеGauss-Seidel MethodВидеоPractice Quiz: Gauss-Seidel Method Задание

Summary

Wrap-up: Numerical Solution of Linear SystemsВидео
06Modeling with Linear Programming27 материалов

Introduction to Optimization

What is Optimization?ВидеоPractice Quiz: What is Optimization? ЗаданиеOptimization ModelsВидеоPractice Quiz: Optimization Models ЗаданиеAdditional Reading: Introduction to OptimizationЧтение

What is Linear Programming Problem (LPP)?

Introduction to LPPВидеоPractice Quiz: Introduction to LPP ЗаданиеConcepts of Linear Function and Linear InequalityВидеоPractice Quiz: Concepts of Linear Function and Linear Inequality Задание What is Linear Programming Problem (LPP)?ЧтениеTranslating Real-World Problems into Linear Programming ModelsDIALOGUE

Formulation of an Linear Programming Problem

Steps of an LP Formulation ВидеоPractice Quiz: Steps of an LP Formulation ЗаданиеBasic Assumptions of an LPPВидеоPractice Quiz: Basic Assumptions of an LPP ЗаданиеFormulation of an LPPЧтение

Linear Programming Applications

Linear Programming Applications: InvestmentВидеоPractice Quiz: Linear Programming Applications: Investment ЗаданиеLinear Programming Applications: Workforce PlanningВидеоPractice Quiz: Linear Programming Applications: Workforce Planning ЗаданиеLinear Programming Applications: Urban Development PlanningВидеоPractice Quiz: Linear Programming Applications: Urban Development Planning Задание

Summary and Assessment

Wrap-Up: Modeling with Linear ProgrammingВидеоTest Yourself: Linear Systems and Linear ProgrammingЗадание
07Graphical Solution and Convex Set35 материалов

Feasible Region

Feasible SolutionВидеоPractice Quiz: Feasible Solution ЗаданиеSketching of Linear InequalitiesВидеоPractice Quiz: Sketching of Linear Inequalities ЗаданиеSketching of Feasible RegionВидеоPractice Quiz: Sketching of Feasible Region ЗаданиеDetermination of the Corner Point of Feasible RegionВидеоPractice Quiz: Determination of the Corner Point of Feasible Region ЗаданиеFeasible RegionЧтение

Convex Set and LP Theory

Some Basic DefinitionsВидеоPractice Quiz: Some Basic Definitions ЗаданиеDefinition of Convex Linear CombinationВидеоPractice Quiz: Definition of Convex Linear Combination ЗаданиеDefinition of Convex Set and Extreme PointВидеоPractice Quiz: Definition of Convex Set and Extreme Point Задание

Graphical Solution of LPP

Steps in Graphical SolutionВидеоPractice Quiz: Steps to Formulate a Graphical Solution ЗаданиеExamples of Graphical Solution of an LPPВидеоPractice Quiz: Examples of Graphical Solution ЗаданиеAdditional Examples of Graphical Solution of an LPPВидеоPractice Quiz: Additional Examples of the Graphical Method Задание

Special Cases in the Graphical Method

Alternative Optimum SolutionsВидеоPractice Quiz: Alternative Optimum Solutions ЗаданиеUnbounded SolutionsВидеоPractice Quiz: Unbounded Solutions ЗаданиеInfeasible SolutionsВидеоPractice Quiz: Infeasible Solutions Задание

Summary

Wrap-up: Graphical Solution and Convex SetВидео
08Simplex Method32 материалов

Transition from Graphical to Algebraic Solution

LP Model in Equation Form: Part 1ВидеоLP Model in Equation Form: Part 2ВидеоPractice Quiz: LP Model in Equation Form ЗаданиеBasic Solution and Basic Feasible SolutionВидеоPractice Quiz: Basic Solution and Basic Feasible Solution ЗаданиеEnumeration of All Basic Solutions of an LPP Through an ExampleВидеоPractice Quiz: Enumeration of All Basic Solutions of an LPP Through an Example ЗаданиеFrom Extreme Points to Basic SolutionsВидеоPractice Quiz: From Extreme Points to Basic Solutions ЗаданиеTransition from Graphical to Algebraic SolutionЧтение

The Simplex Method

Iterative Nature of the Simplex MethodВидеоPractice Quiz: Iterative Nature of the Simplex Method ЗаданиеThe Algebra of the Simplex MethodВидеоPractice Quiz: The Algebra of the Simplex Method ЗаданиеComputational Details of the Simplex MethodВидеоPractice Quiz: Computational Details of the Simplex Method Задание

Simplex Method Fundamentals

Generalized Simplex Tableau in a Matrix FormВидеоPractice Quiz: Generalized Simplex Tableau in a Matrix Form ЗаданиеExplanation of the Simplex Table in a Matrix Form: Part 1ВидеоPractice Quiz: Explanation of the Simplex Table in a Matrix Form: Part 1 ЗаданиеExplanation of the Simplex Table in a Matrix Form: Part 2ВидеоPractice Quiz: Explanation of the Simplex Table in a Matrix Form: Part 2 Задание

Summary and Assessment

Wrap-Up: Simplex MethodВидеоTest Yourself: Solving Linear Programming ProblemsЗадание
09Artificial Starting Solution and Special Cases in the Simplex Method26 материалов

Artificial Starting Solution

Need for Artificial VariableВидеоPractice Quiz: Need for Artificial Variable ЗаданиеIntroduction of the M-MethodВидеоPractice Quiz: Introduction of the M-Method ЗаданиеConstruction of Initial Tableau of the M-MethodВидеоPractice Quiz: Construction of Initial Tableau of the M-Method ЗаданиеComputational Aspects of the M-MethodВидеоPractice Quiz: Computational Aspects of the M-Method ЗаданиеReading: Artificial Variables and the M-Method ЧтениеIntroduction of the Two-Phase MethodВидеоPractice Quiz: Introduction of the Two-Phase Method ЗаданиеComputational Aspects of Phase IВидеоPractice Quiz: Computational Aspects of Phase I ЗаданиеIntroduction of Phase IIВидеоPractice Quiz: Introduction of Phase II ЗаданиеAdditional Reading: Artificial Starting SolutionЧтение

Special Cases in the Simplex Method

Simplex Method: DegeneracyВидеоPractice Quiz: Simplex Method: Degeneracy ЗаданиеSimplex Method: Unbounded SolutionsВидеоPractice Quiz: Simplex Method: Unbounded Solutions ЗаданиеSimplex Method: Alternative Optimal SolutionsВидеоPractice Quiz: Simplex Method: Alternative Optimal Solutions Задание

Summary

Wrap-Up: Artificial Starting Solution and Special Cases in the Simplex MethodВидео
10Duality and Dual Simplex Method29 материалов

Duality

Introduction to a Dual Problem Through ExampleВидеоPractice Quiz: Introduction to a Dual Problem Through Example ЗаданиеDual Problem: Few ObservationsВидеоPractice Quiz: Dual Problem: Few Observations ЗаданиеExample of a Dual Problem ConstructionВидеоPractice Quiz: Example of a Dual Problem Construction ЗаданиеFinding the Dual in GeneralВидеоPractice Quiz: Finding the Dual in General ЗаданиеThe Fundamental Duality PropertiesВидеоPractice Quiz: The Fundamental Duality Properties ЗаданиеHow to Find Optimal Solution of DualВидеоPractice Quiz: How to Find Optimal Solution of Dual ЗаданиеExample of an Optimal Solution of DualВидеоPractice Quiz: Example of an Optimal Solution of Dual ЗаданиеAdditional Examples of DualityВидеоPractice Quiz: Additional Examples of Duality ЗаданиеDualityЧтение

The Dual Simplex Method

Description of the Dual Simplex MethodВидеоPractice Quiz: Description of the Dual Simplex Method ЗаданиеFeasibility Test and Iteration of the Dual Simplex MethodВидеоPractice Quiz: Feasibility Test and Iteration of the Dual Simplex Method ЗаданиеSolution by Dual Simplex Method: An ExampleВидеоPractice Quiz: Solution by Dual Simplex Method: An Example Задание

Summary and Assessment

Wrap-up: Duality and Dual Simplex MethodВидеоTest Yourself: Artificial Variables, Duality and Dual Simplex MethodЗадание

Course Wrap Up

Course SummaryЧтение
Row Reduction Algorithm: Part 1Видео
Row Reduction AlgorithmЗадание
Row Reduction Algorithm: Part 2Видео
Row Reduction AlgorithmЗадание
Existence and Uniqueness TheoremВидео
Existence and Uniqueness Theorem Задание
Additional Readings: Row Reduction and Echelon FormsЧтение
Solving Linear System Using Cramer's RuleВидео
Solving Linear System Using Cramer's Rule Задание
Additional Readings: Solving Linear System Using Inverse of a MatrixЧтение
Definition of a Linear TransformationВидео
Definition of a Linear Transformation Задание
Additional Readings: Null Spaces, Column Spaces, and Linear TransformationЧтение
Видео
Bases for Nul A and Col A Задание
Additional Readings: Linearly Independent Sets Чтение
Identifying Linear Independence and Basis ConstructionDIALOGUE
Чтение
Examples on LU DecompositionВидео
Practice Quiz: Examples on LU Decomposition Задание
LU DecompositionЧтение
Choosing the Right Numerical Method for Linear SystemsDIALOGUE
Examples of Gauss-Seidel MethodВидео
Practice Quiz: Examples of Gauss-Seidel Method Задание
Iterative Methods for Linear SystemsЧтение
Linear Programming Applications: BlendingВидео
Practice Quiz: Linear Programming Applications: Blending Задание
Additional Reading: Linear Programming ApplicationsЧтение
Few Results on Convex SetsВидео
Practice Quiz: Few Results on Convex Sets Задание
Application of an LPPВидео
Practice Quiz: Application LPP Задание
Convex Set and LP TheoryЧтение
Graphical Solution of LPP Чтение
Special Cases in the Graphical MethodЧтение
Summary of the Simplex MethodВидео
Practice Quiz: Summary of the Simplex Method Задание
Additional Examples of Solving an LPP Using the Simplex MethodВидео
Practice Quiz: Additional Examples of Solving an LPP Using the Simplex Method Задание
The Simplex MethodЧтение
Example of a Simplex Table in a Matrix FormВидео
Practice Quiz: Example of a Simplex Table in a Matrix Form Задание
Simplex Method FundamentalsЧтение
Simplex Method: Infeasible SolutionsВидео
Practice Quiz: Simplex Method: Infeasible Solutions Задание
Special Cases in the Simplex MethodЧтение
Identification of the Infeasible SolutionВидео
Practice Quiz: Identification of the Infeasible Solution Задание
The Dual Simplex MethodЧтение