Overview

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.

Syllabus

Matrices

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.

Solving Linear Systems

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.

Vector Spaces and Linear Transformations

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.

Eigenvalues and Eigenvectors

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.

Numerical Solution of Linear Systems

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.

Modeling with Linear Programming

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.

Graphical Solution and Convex Set

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.

Simplex Method

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.

Artificial Starting Solution and Special Cases in the Simplex Method

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.

Duality and Dual Simplex Method

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.