Birla Institute of Technology & Science, Pilani

Linear Algebra for Machine Learning & AI

Birla Institute of Technology & Science, Pilani

Linear Algebra for Machine Learning & AI

This course is part of Mathematics for Engineering Specialization

BITS Pilani Instructors Group

Instructor: BITS Pilani Instructors Group

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Gain insight into a topic and learn the fundamentals.
Beginner level

Recommended experience

4 weeks to complete
at 10 hours a week
Flexible schedule
Learn at your own pace
Gain insight into a topic and learn the fundamentals.
Beginner level

Recommended experience

4 weeks to complete
at 10 hours a week
Flexible schedule
Learn at your own pace

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.

Details to know

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Assessments

127 assignments

Taught in English

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This course is part of the Mathematics for Engineering Specialization
When you enroll in this course, you'll also be enrolled in this Specialization.
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  • Gain a foundational understanding of a subject or tool
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There are 10 modules in this course

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

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

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

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

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

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

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

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

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

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

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Instructor

BITS Pilani Instructors Group
Birla Institute of Technology & Science, Pilani
30 Courses 58,730 learners

Offered by

Birla Institute of Technology & Science, Pilani

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