Linear Algebra for Data Science & Machine Learning A-Z 2024 from Udemy

What's inside

Learning objectives

Fundamentals of linear algebra and how to ace your linear algebra exam
Basics of matrices (notation, dimensions, types, addressing the entries etc.)
Operations on a single matrix, e.g. scalar multiplication, transpose, determinant & adjoint
Operations on two matrices, including addition, subtraction and multiplication of matrices
Performing elementary row operations and finding echelon forms (ref & rref)
Inverses, including invertible and singular matrices, and the cofactor method
Solving systems of linear equations using matrices and inverse matrices, including cramer’s rule to solve ax = b
Properties of determinants, and how to perform gauss-jordan elimination
Matrices as vectors, including vector addition and subtraction, head-to-tail rule, components, magnitude and midpoint of a vector

Vector spaces, including dimensions, euclidean spaces, closure properties and axioms
Linear combinations and span, spanning set for a vector space and linear dependence
Subspace and null-space of a matrix, matrix-vector products
Basis and standard basis, and checking if a set of given vectors forms the basis for a vector space
Eigenvalues and eigenvectors, including how to find eigenvalues and the corresponding eigenvectors
Basic algebra concepts ( as a bonus)
And so much more…..
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Fundamentals of linear algebra and how to ace your linear algebra exam
Basics of matrices (notation, dimensions, types, addressing the entries etc.)
Operations on a single matrix, e.g. scalar multiplication, transpose, determinant & adjoint
Operations on two matrices, including addition, subtraction and multiplication of matrices
Performing elementary row operations and finding echelon forms (ref & rref)
Inverses, including invertible and singular matrices, and the cofactor method
Solving systems of linear equations using matrices and inverse matrices, including cramer’s rule to solve ax = b
Properties of determinants, and how to perform gauss-jordan elimination
Matrices as vectors, including vector addition and subtraction, head-to-tail rule, components, magnitude and midpoint of a vector
Vector spaces, including dimensions, euclidean spaces, closure properties and axioms
Linear combinations and span, spanning set for a vector space and linear dependence
Subspace and null-space of a matrix, matrix-vector products
Basis and standard basis, and checking if a set of given vectors forms the basis for a vector space
Eigenvalues and eigenvectors, including how to find eigenvalues and the corresponding eigenvectors
Basic algebra concepts ( as a bonus)
And so much more…..
Show more
Show less

Syllabus

Welcome and Introduction

This video is to officially welcome you to the Linear Algebra course. I give an overview of the topics covered, and the strategies to get the most out of this course!

SOLUTIONS of Assignments

Basics of Matrices

Matrices and their Significance - 001

Matrix Notation - 002

Dimension (Order) of a Matrix - 003

In this quiz, we practice how to specify the Dimensions of a Matrix.

Addressing Elements of a Matrix - 004

In this quiz, we practice how to address or refer to the elements of a matrix.

Solving Linear Systems in 2 Unknowns - 005

In this quiz, we practice how to solve systems of 2 linear equations in 2 unknowns, without using matrices.

Solving Linear Systems in 3 Unknowns - 006

In this quiz, we practice how to solve systems of 3 linear equations in 3 unknowns, without using matrices.

In this section, we summarize basics of Matrices, e.g. Order of a Matrix, Addition, Subtraction and Multiplication of Matrices, Determinants and Inverse for 2x2 matrices, and Simultaneous Equations.

IMPORTANT - This section is OPTIONAL

Types of Matrices

Addition and Subtraction of Matrices

Multiplication of Scalars with Matrices

Multiplication of two Matrices

Inverse and Determinant of a 2x2 Matrix

The Formula: Inverse (A) = Adjoint (A) / Determinant (A)

* EXAMPLE - Inverse of a 2x2 Matrix

Using Matrices to Solve Simultaneous Linear Equations

* EXAMPLE - Using Matrices to Solve Simultaneous Linear Equations

CHALLENGE QUESTION - Using Matrices to Solve Simultaneous Linear Equations

SUMMARY

Matrices and Systems of Linear Equations

https://matrix.reshish.com/

In this lesson of the Linear Algebra course, we look at how to represent a system of 2 linear equations in the 2x2 Matrix form.

In this lesson of the Linear Algebra course, we look into how to write a system of 3 linear equations in the form of a 3x3 matrix and solve it.

In this lesson of the Linear Algebra course, we see how to perform different types of row operations on a matrix to convert it into Row Echelon Form (REF).

In this lesson of the Linear Algebra course, we learn what the Row Echelon Form (REF) of a matrix is, and how to compute it.

In this lesson of the Linear Algebra course, we learn what the Reduced Row Echelon Form (RREF) of a matrix is, and how to obtain it.

* ASSIGNMENT 1: Matrices and Linear Equations

Matrix Algebra and Operations

In this lesson of the Linear Algebra course, we learn how to perform addition and subtraction of matrices.

In this lesson of the Linear Algebra course, we learn how a scalar can be multiplied to a matrix, and what are the rules for that.

In this lesson of the Linear Algebra course, multiplication of two matrices with each other is explained, using examples.

In this lesson of the Linear Algebra course, we learn how to get transpose of a given matrix.

** ASSIGNMENT 2: Matrix Algebra & Operations

Students will learn to compute determinant of a given matrix.

In this lesson of the Linear Algebra course, we learn how to compute determinant of a 2x2 matrix.

In this lesson of the Linear Algebra course, we learn how to compute determinant of a 3x3 matrix.

In this lesson of the Linear Algebra course, I discuss some shortcuts that we can possibly use in certain cases to find determinants quickly and easily.

*** ASSIGNMENT 3: Computing Determinants

Inverse of a Matrix

In this lesson of the Linear Algebra course, we learn why inverse can be calculated only for square matrices, and why inverse doesn't exist for non-square matrices.

In this lesson of the Linear Algebra course, we learn what the term Singular Matrix means, and how is it related to the inverse of a matrix.

In this lesson of the Linear Algebra course, we see why finding inverse of the coefficient matrix is important and helpful for solving a linear system.

Inverse of a 2x2 Matrix

Inverse of a 3x3 Matrix - The Two Methods

Inverse of a 3x3 Matrix - The Co-factor Method

Inverse of a 3x3 Matrix - Gauss-Jordan Elimination Method

Properties of Determinants

In this lesson of the Linear Algebra course, we look at the property of the determinants that deals with the matrix row operation 1.

In this lesson of the Linear Algebra course, we look at the property of the determinants that deals with the matrix row operation 2.

In this lesson of the Linear Algebra course, we look at the property of the determinants that deals with the matrix row operation 3.

In this lesson of the Linear Algebra course, we summarize the properties of the determinants that deal with the matrix row operations.

In this lesson of the Linear Algebra course, we apply our knowledge of the properties of determinants.

In this lesson of the Linear Algebra course, we look at one more property of the matrix determinants that is very helpful..

*** OPTIONAL: Introduction to Vectors

Introduction to the Section

Scalars and Vectors

Geometrical Representation of Vectors

Vector Addition and Subtraction

Laws of Vector Addition and Head to Tail Rule

Unit Vector

Components of a Vector in 2D

Position Vector

3-D Vectors and Magnitude of a Vector

Displacement Vector

Finding Midpoint using Vectors

Vector Spaces

In this lesson of the Linear Algebra course, you are introduced to the Vector Spaces.

In this lesson of the Linear Algebra course, we discuss what Euclidean vector spaces are.

In this lesson of the Linear Algebra course, Euclidean vector spaces are discussed in further detail, in continuation of the previous lesson.

In this lesson of the Linear Algebra course, further explanation is provided on the topic of Euclidean vector spaces.

In this lesson of the Linear Algebra course, we look into what Closure Properties are, and how these are used as a criteria to check for vector spaces.

In this lesson of the Linear Algebra course, the ten fundamental axioms for vector spaces are listed and explained.

In this lesson of the Linear Algebra course, examples of closure properties are discussed.

In this lesson of the Linear Algebra course, we discuss an example of vector spaces to clarify the concept.

In this lesson of the Linear Algebra course, one more example of vector spaces is discussed.

Subspace and Nullspace

In this lesson of the Linear Algebra course, you are introduced to the topic of Subspaces.

In this lesson of the Linear Algebra course, subspaces are explained with the help of example 1.

In this lesson of the Linear Algebra course, subspaces are further explained with the help of example 2.

In this lesson of the Linear Algebra course, subspaces are further explained with the help of example 3.

In this lesson of the Linear Algebra course, the topic of Nullspace of a matrix is discussed and explained..

In this lesson of the Linear Algebra course, nullspaces are further explained with the help of an example.

**** ASSIGNMENT 4: Vector Spaces, Subspaces and Null Spaces

Span and Spanning Sets

In this lesson of the Linear Algebra course, we discuss what does the span of a set of given vectors means, and how to compute that.

In this lesson of the Linear Algebra course, we further discuss the span of a set of given vectors through an example.

In this lesson of the Linear Algebra course, we discuss the notion of spanning set for a vector space using a few examples.

In this lesson of the Linear Algebra course, spanning sets are further explained with the help of example 3.

In this lesson of the Linear Algebra course, spanning sets are further explained with the help of example 4.

Linear Dependence and Independence

In this lesson of the Linear Algebra course, we look into the notion of linear dependence and linear independence.

In this lesson of the Linear Algebra course, formal definition of linear dependence is presented and discussed.

Good to know

Know what's good

, what to watch for

, and possible dealbreakers

Teaches Algebra basics suitable for students and professionals

Relevant for lucrative careers in Data Science and Machine Learning

Provides ample practice in each topic via solved examples, quizzes, and assignments

Covers multiple aspects of Linear Algebra, from basic to advanced

Includes a bonus section on basic Algebra concepts

Instructor has over 10 years of experience teaching Math and Engineering

Reviews summary

Intuitive linear algebra

Learners say this course is a great way to develop intuition for complex concepts with engaging assignments and a helpful instructor. Although the course content is engaging and provides clear explanations, providing more detailed assignment solutions could improve the learning process.

Instructor answers questions in a clear way.

"I asked many questions in the forum and He always gave answers that were clear and helped me understand the material."

Explanations were clear.

"Kashif's explanations and examples are very clear."

"I definitely developed intuition for concepts I didn't know much about before."

Exams could be difficult.

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Linear Algebra for Data Science & Machine Learning A-Z 2024 with these activities:

Attend a Math Club Meeting

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This course is a great opportunity to meet other students who are interested in math, including linear algebra.

Browse courses on Linear Algebra

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Find a local math club and attend a meeting.
Introduce yourself to other students and ask them about their interests.
Talk to the club advisor about your goals for learning linear algebra.

Review Linear Algebra and Its Applications

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To be successful in this course, it is important for you to have a strong basis in the theory of Linear Algebra, which this textbook provides.

View Linear Algebra for Everyone on Amazon

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Start by reading the introduction to Linear Algebra and its applications.
Next, read the chapters on matrices, vectors, and systems of linear equations.
Finally, read the chapters on eigenvalues and eigenvectors, and on applications of linear algebra.

Practice Solving Systems of Linear Equations

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To be successful in this course, it is important for you to be able to solve systems of linear equations. This activity will give you the practice you need.

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Start by solving some simple systems of linear equations.
Then, try to solve some more challenging systems.
Finally, try to solve some systems of linear equations that involve complex numbers.

Three other activities

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Show all six activities

Form a Study Group

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This course is challenging, but it is more fun, and more achievable, when you study with friends.

Browse courses on Linear Algebra

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Find a group of students who are also taking this course.
Meet regularly to discuss the course material.
Work together on problem sets and projects.

Participate in a Math Competition

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This competition is a great way to test your skills in linear algebra and to meet other students with similar interests.

Browse courses on Linear Algebra

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Find a math competition that you are interested in participating in.
Register for the competition and start preparing.
Take the competition and see how you do.

Develop a Linear Algebra Project

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This project will allow you to apply the concepts of linear algebra to a real-world problem.

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Start by choosing a topic for your project.
Next, develop a plan for your project and outline the steps that you will take to complete it.
Finally, write a report on your project and present it to the class.

Career center

Learners who complete Linear Algebra for Data Science & Machine Learning A-Z 2024 will develop knowledge and skills that may be useful to these careers:

Data Scientist

Data Scientists use statistical techniques to analyze vast amounts of data and help businesses make informed decisions. This course covers topics such as linear algebra, matrices, and determinants, which are essential for understanding and working with data. By taking this course, you will gain the skills and knowledge necessary to succeed as a Data Scientist.

See salaries and explore the career path for Data Scientist

Machine Learning Engineer

Machine Learning Engineers design and develop machine learning systems. This course covers topics such as linear algebra and matrix algebra, which are essential for understanding and working with machine learning algorithms. By taking this course, you will gain the skills and knowledge necessary to succeed as a Machine Learning Engineer.

See salaries and explore the career path for Machine Learning Engineer

Operations Research Analyst

Operations Research Analysts use mathematical and statistical techniques to solve optimization problems in a variety of industries. This course covers topics such as linear algebra and matrix algebra, which are essential for understanding and working with optimization models. By taking this course, you will gain the skills and knowledge necessary to succeed as an Operations Research Analyst.

See salaries and explore the career path for Operations Research Analyst

Statistician

Statisticians use mathematical and statistical techniques to collect, analyze, and interpret data. This course covers topics such as linear algebra and matrix algebra, which are essential for understanding and working with statistical data. By taking this course, you will gain the skills and knowledge necessary to succeed as a Statistician.

See salaries and explore the career path for Statistician

Data Analyst

Data Analysts use statistical techniques to analyze data and help businesses make informed decisions. This course covers topics such as linear algebra, matrices, and determinants, which are essential for understanding and working with data. By taking this course, you will gain the skills and knowledge necessary to succeed as a Data Analyst.

See salaries and explore the career path for Data Analyst

Financial Analyst

Financial Analysts use mathematical and statistical techniques to analyze financial data and make investment decisions. This course covers topics such as linear algebra and matrix algebra, which are essential for understanding and working with financial data. By taking this course, you will gain the skills and knowledge necessary to succeed as a Financial Analyst.

See salaries and explore the career path for Financial Analyst

Quantitative Analyst

Quantitative Analysts use mathematical and statistical techniques to analyze financial data and make investment decisions. This course covers topics such as linear algebra and matrix algebra, which are essential for understanding and working with financial data. By taking this course, you will gain the skills and knowledge necessary to succeed as a Quantitative Analyst.

See salaries and explore the career path for Quantitative Analyst

Actuary

Actuaries use mathematical and statistical techniques to assess risk and uncertainty in the insurance and finance industries. This course covers topics such as linear algebra and matrix algebra, which are essential for understanding and working with insurance and financial data. By taking this course, you will gain the skills and knowledge necessary to succeed as an Actuary.

See salaries and explore the career path for Actuary

Software Engineer

Software Engineers design and develop software applications. This course covers topics such as linear algebra and matrix algebra, which are essential for understanding and working with software algorithms. By taking this course, you will gain the skills and knowledge necessary to succeed as a Software Engineer.

See salaries and explore the career path for Software Engineer

Computer Scientist

Computer Scientists research and develop new computer technologies. This course covers topics such as linear algebra and matrix algebra, which are essential for understanding and working with computer algorithms. By taking this course, you will gain the skills and knowledge necessary to succeed as a Computer Scientist.

See salaries and explore the career path for Computer Scientist

Mathematician

Mathematicians study the properties and applications of numbers, shapes, and other abstract concepts. This course covers topics such as linear algebra and matrix algebra, which are essential for understanding and working with mathematical concepts. By taking this course, you will gain the skills and knowledge necessary to succeed as a Mathematician.

See salaries and explore the career path for Mathematician

Financial Manager

Financial Managers plan and direct the financial activities of organizations. This course covers topics such as linear algebra and matrix algebra, which are essential for understanding and working with financial data. By taking this course, you will gain the skills and knowledge necessary to succeed as a Financial Manager.

See salaries and explore the career path for Financial Manager

Economist

Economists study the production, distribution, and consumption of goods and services. This course covers topics such as linear algebra and matrix algebra, which are essential for understanding and working with economic models. By taking this course, you will gain the skills and knowledge necessary to succeed as an Economist.

See salaries and explore the career path for Economist

Physicist

Physicists study the laws of nature and the universe. This course covers topics such as linear algebra and matrix algebra, which are essential for understanding and working with physical concepts. By taking this course, you will gain the skills and knowledge necessary to succeed as a Physicist.

See salaries and explore the career path for Physicist

Teacher

Teachers educate students at all levels, from preschool to university. This course covers topics such as linear algebra and matrix algebra, which are essential for understanding and working with educational concepts. By taking this course, you will gain the skills and knowledge necessary to succeed as a Teacher.

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