# 10 Best Linear Algebra Courses For Beginners in 2023

Linear algebra is a foundational mathematical subject essential for many fields, including computer science, engineering, physics, and data science. If you are a beginner in linear algebra, you might wonder where to begin. There are many great online courses available that can help you learn the basics of linear algebra.

Keeping this in mind, here at Coursesity, we have curated some of the Best Linear Algebra Courses & Tutorials for beginners. These courses are offered by top universities and online learning platforms taught by experts. They cover various topics, from vectors and matrices to eigenvalues and eigenvectors.

Whether you are a complete beginner or have some prior knowledge of linear algebra, we are confident that you will find one of these courses helpful. So what are you waiting for? Start learning today!

## Top Linear Algebra Courses Online List

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## 1. Become a Linear Algebra Master

This course is a comprehensive learning program consisting of 247 lessons covering all essential linear algebra topics. It is specifically designed to equip students with a solid understanding of linear algebra concepts and their practical applications. Whether you are a beginner or have some prior knowledge, this course will take you from the fundamentals to advanced topics systematically and engagingly.

In this Linear Algebra course, you will learn the following:

• Operations on one matrix, including solving linear systems, and Gauss-Jordan elimination.
• Operations on two matrices, including matrix multiplication and elimination matrices.
• Matrices as vectors, including linear combinations and spans, linear independence, and subspaces.
• Dot products and cross products, including the Cauchy-Schwarz and vector triangle inequalities.
• Matrix-vector products, including the null and column spaces, and solving Ax=b.
• Transformations, including linear transformations, projections, and composition of transformations.
• Inverses, including invertible and singular matrices, and solving systems with inverse matrices.
• Determinants, including upper and lower triangular matrices, and Cramer's rule.
• Transposes, including their determinants, and the null (left null) and column (row) spaces of the transpose.
• Orthogonality and change of basis, including orthogonal complements, projections onto a subspace, least squares, and changing the basis.
• Orthonormal bases and Gram-Schmidt, including the definition of the orthonormal basis, and converting to an orthonormal basis with the Gram-Schmidt process.
• Eigenvalues and Eigenvectors, including finding eigenvalues and their associate eigenvectors and eigenspaces, and eigen in three dimensions.

The course includes a combination of video and text explanations to cater to various learning preferences. With 69 quizzes and detailed solutions, as well as 12 workbooks packed with additional practice problems, you will have ample opportunities to test your understanding and reinforce your skills.

• Course rating: 4.8 out of 5.0 (4,396 Rating total)
• Duration: 15 Hours
• Certificate: Certificate on completion

## 2. Mathematics for Machine Learning: Linear Algebra

This course is designed to provide students with a comprehensive understanding of linear algebra and its practical applications in data analysis and machine learning. It goes beyond theoretical concepts and focuses on how linear algebra relates to real-world data problems.

In this Linear Algebra course, you will learn the following topics:

• Week 1 - Introduction to Linear Algebra and to Mathematics for Machine Learning.
• Week 2 - Vectors are objects that move around space.
• Week 3 - Matrices in Linear Algebra: Objects that operate on Vector.
• Week 4 - Matrices make linear mappings.
• Week 5 - Eigenvalues and Eigenvectors: Application to Data Problems.

This course introduces linear algebra concepts related to vectors and matrices. You will learn to manipulate and work with vectors and matrices, including solving the challenging problems of eigenvalues and eigenvectors. These concepts serve as powerful tools for problem-solving in various data-driven applications.

As the course progresses, you will explore exciting linear algebra applications in working with datasets. Topics covered include image rotation, eigenvector analysis, and the implementation of the Pagerank algorithm. These examples demonstrate firsthand how linear algebra is crucial in extracting meaningful insights from data.

The course will enable you to solve complex problems in linear algebra and apply these concepts effectively in machine learning by the end of the course. Whether you're a beginner or seeking to enhance your data analysis skills, this course will equip you with the necessary knowledge to excel in data-driven applications.

• Course rating: 4.7 out of 5.0 (11,540 Rating total)
• Duration: 18 Hours
• Certificate: Certificate on completion

## 3. Complete Linear Algebra: Theory and Implementation in Code

Learn concepts in linear algebra and matrix analysis, and implement them in MATLAB and Python. The course offers a unique and effective approach to mastering linear algebra concepts and their practical applications. Moreover, it explains key principles clearly and comprehensively, ensuring that fundamental principles are well understood.

In this Linear Algebra course, you will learn the following:

• Understand theoretical concepts in linear algebra, including proofs.
• Implement linear algebra concepts in scientific programming languages (MATLAB, Python).
• Apply linear algebra concepts to real datasets.
• Ace your linear algebra exam!
• Apply linear algebra on computers with confidence.
• Gain additional insights into solving problems in linear algebra, including homework and applications.
• Be confident in learning advanced linear algebra topics.
• Understand some of the important maths underlying machine learning.
• The math underlying most AI (artificial intelligence).

In addition to mastering linear algebra, this course also focuses on improving coding skills for scientific and data analysis purposes. While elementary Python or MATLAB is not taught, the course guides students in enhancing their programming skills through the application of linear algebra concepts.

By the end of this comprehensive course, you will have a strong foundation in linear algebra, practical coding skills, and the ability to apply these concepts to real-world scenarios. Whether you are a beginner or looking to refine your knowledge, this course provides a comprehensive and immersive learning experience.

• Course rating: 4.8 out of 5.0 (4,159 Rating total)
• Duration: 34 Hours
• Certificate: Certificate on completion

## 4. Linear Algebra for Machine Learning and Data Science

This beginner-friendly program addresses the common challenge faced by machine learning engineers and data scientists who require a solid foundation in mathematics. Even experienced practitioners can benefit from strengthening their math skills to unlock their full potential. The program adopts innovative pedagogy and visualization techniques to facilitate quick and intuitive learning, allowing learners to grasp the underlying mathematics of machine learning.

In this Linear Algebra course, you will learn the following:

• Represent data as vectors and matrices and identify their properties using concepts of singularity, rank, and linear independence.
• Apply common vector and matrix algebra operations like the dot product, inverse, and determinants.
• Express certain types of matrix operations as a linear transformation, and apply concepts of eigenvalues and eigenvectors to machine learning problems.

You will learn the fundamentals of machine learning and data analysis. The curriculum covers topics such as representing data as vectors and matrices and identifying properties like singularity, rank, and linear independence. You will also learn to apply common vector and matrix algebra operations, including dot product, inverse, and determinants. Moreover, one of the key highlights of the program is the application of eigenvalues and eigenvectors to machine learning problems.

Upon completion of the course, you will understand the mathematics behind the most commonly used machine learning algorithms. It will equip you with the confidence to integrate these mathematical concepts into your career in machine learning. Regardless of your level of experience or interest in machine learning and data science, this program will provide you with the tools and knowledge you need to excel.

• Course rating: 4.4 out of 5.0 (351 Rating total)
• Duration: 21 Hours
• Certificate: Certificate on completion

## 5. Learn Algebra The Easy Way

The Linear Algebra course is designed to cater to the needs of university students taking intermediate algebra and college algebra, as well as high school students enrolled in Algebra 1, Algebra 2, or Algebra 3. This course provides a thorough and accessible exploration of essential algebraic concepts and techniques.

Throughout the course, learners will cover a wide range of topics, building a strong foundation in algebra. Starting with basic arithmetic operations such as addition, subtraction, multiplication, and division, the course progresses to more complex areas of algebraic study.

Key topics covered in the course include fractions review, solving linear equations (single-step and multi-step equations with variables and parentheses), order of operations (PEMDAS), absolute value functions and inequalities, graphing linear equations using slope and the y-intercept, polynomials (addition, subtraction, multiplication, and division), and factoring techniques (difference of perfect squares, trinomials, sum and difference of perfect cubes, etc.).

By the end of the course, learners will have acquired a solid understanding of algebraic principles, techniques, and applications. They will be equipped to tackle algebraic problems and demonstrate proficiency in graphing, solving equations, and working with various types of functions. This comprehensive algebra course serves as a stepping stone for further studies in mathematics and related fields.

• Course rating: 4.7 out of 5.0 (1,508 Rating total)
• Duration: 21 Hours
• Certificate: Certificate on completion

## 6. Essential Linear Algebra for Data Science

This course focuses on teaching you the essential principles of Linear Algebra specifically tailored for a career in Data Science. Consider this course your expressway to Data Science, providing accessible methods and user-friendly explanations that will enable you to master Linear Algebra.

In this Linear Algebra course, you will learn the following:

• Solve real-world problems using the foundational concept of matrices and explain where those problems might arise.
• Recognize what a matrix represents in n-dimensional space and how transformations act in that space.
• Identify key properties of any system of equations, such as independence, basis, rank, and more, and what they mean for the overall system.
• Demonstrate your understanding of projections in lower dimensions while being able to carry out higher-dimension projections for real-world problems.

This course is designed to prepare learners to complete Statistical Modeling for Data Science Application, which is part of CU Boulder's Master of Science in Data Science (MS-DS) program.

• Course rating: 4.6 out of 5.0 (86 Rating total)
• Duration: 7 Hours
• Certificate: Certificate on completion

## 7. Linear Algebra for Data Science & Machine Learning A-Z 2023

The course will prepare you to understand and apply the fundamental concepts and linear algebra techniques. It will help you excel in your exams and understand this essential mathematical discipline. As a result of practical examples and interactive exercises, you will demonstrate a deep understanding of linear algebra enabling you to apply these skills in various real-world situations.

In this Linear Algebra course, you will learn the following:

• 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 the 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.

The course also explores the concept of matrices as vectors. It covers topics like vector addition and subtraction, the Head-to-Tail rule, and components, magnitudes, and midpoints of vectors. You will gain a deep understanding of linear combinations of matrices, spans, and vector spaces (including dimensions and closure properties), and the concepts of subspace and null space of a matrix. The course also provides insights into matrix-vector products, spanning sets for vector spaces, and linear dependence.

One of the key highlights of the course is its focus on solving systems of equations using matrices and inverse matrices. You will master techniques such as Gauss-Jordan elimination and the utilization of Cramer's rule to solve AX = B. Moreover, the course delves into the properties of determinants and provides insights on how to leverage them effectively.

• Course rating: 4.6 out of 5.0 (706 Rating total)
• Duration: 18 Hours
• Certificate: Certificate on completion

## 8. Linear Algebra and Geometry 1

This Linear Algebra course, divided into four chapters, equips you with essential knowledge and skills to solve real-world problems, understand geometric interpretations, and apply linear algebra concepts in mathematics, natural sciences, and analytical geometry.

In this Linear Algebra course, you will learn the following:

• How to solve problems in linear algebra and geometry (illustrated with 175 solved problems) and why these methods work.
• Solve systems of linear equations with the help of Gauss-Jordan or Gaussian elimination, the latter followed by back-substitution.
• Interpret geometrical solution sets of systems of linear equations by analyzing their RREF matrix (row equivalent with the augmented matrix of the system).
• Matrix operations (addition, scaling, multiplication), how they are defined, how they are applied, and what computational rules hold for them.
• Matrix inverse: determine whether a matrix is invertible; compute its inverse: both with (Jacobi) algorithm and by the explicit formula; matrix equations.
• Determinants, their definition, properties, and different ways of computing them; determinant equations; Cramer's rule for n-by-n systems of equations.
• Vectors, their coordinates, and norm; geometrical vectors and abstract vectors, their addition and scaling: arithmetically and geometrically (in 2D and 3D).
• Vector products (scaling, dot product, cross product, scalar triple product), their properties and applications; orthogonal projection and vector decomposition.
• Analytical geometry in the 3-space: different ways of describing lines and planes, with applications in problem-solving.
• Compute distances between points, planes, and lines in the 3-space, both by using orthogonal projections and by geometrical reasoning.
• Determine whether lines and planes are parallel, and compute the angles between them (using dot product and directional or normal vectors) if they intersect.
• How to geometrically interpret n-by-2 and n-by-3 systems of equations and their solution sets as intersection sets between lines in 2D or planes in 3D.
• Understand the connection between systems of linear equations and matrix multiplication.
• Invertible Matrix Theorem and its applications; apply the determinant test in various situations.

Here are the four chapters, you will learn in this linear algebra course:

Chapter 1: Systems of Linear Equations

This chapter introduces basic concepts and develops geometric intuition related to linear equations and systems of linear equations. You will learn techniques to solve systems using Gaussian elimination, including cases with unique solutions, inconsistent systems, and systems with infinitely many solutions. The chapter also explores applications of systems of linear equations in mathematics and natural sciences.

Chapter 2: Matrices and Determinants
In this chapter, you will delve into matrices and their operations, including addition, subtraction, scalar multiplication, and matrix multiplication. The concept of matrix inverses and their algebraic properties will be covered, along with the computation of inverses using Gauss-Jordan elimination. The link between linear systems and matrices will be explored. Additionally, you will learn about determinants, their definition, arithmetic laws, and their role in solving systems of linear equations and finding the inverse of non-singular matrices.

Chapter 3: Vectors and Their Products
This chapter focuses on vectors in 2-space, 3-space, and n-space, covering arithmetic operations and graphical illustrations. Distance and norms in R^n, dot product, orthogonality, and orthogonal projections will be discussed. The concept of cross-product and its interpretation as the volume of a parallelepiped in 3-space will also be explored.

Chapter 4: Analytical Geometry of Lines and Planes
This chapter delves into the description of lines and planes in 2D and 3D spaces, including various forms of equations and their computations. The geometry of linear systems and the incidence between lines and planes will be studied. Techniques for determining distances between points, lines, and planes will be covered.

• Course rating: 4.8 out of 5.0 (562 Rating total)
• Duration: 46 Hours
• Certificate: Certificate on completion

## 9. Machine Learning Foundations: Linear Algebra

Have you ever been curious about the fundamental workings of machine learning algorithms? Look no further than linear algebra, the backbone of machine learning. A solid understanding of linear algebra is essential for comprehending and developing various machine learning algorithms, particularly those powering neural networks, natural language processing tools, and deep learning models.

In this Linear Algebra course, you will learn the following topics:

• Introduction to Linear Algebra
• Vectors Basics
• Vector Projections and Basis
• Introduction to Matrices
• Gaussian Elimination
• Matrices from Orthogonality to Gram–Schmidt Process
• Eigenvalues and Eigenvectors

The course explores the fundamental concepts of linear algebra along with the techniques necessary to develop and implement a successful machine-learning algorithm. You will discover the basics of vector arithmetic, vector norms, matrix properties, advanced operations, matrix transformation, and algorithms like Google PageRank. By the end of this course, you’ll be ready to take the principles of linear algebra and apply them to your next big machine-learning project.

• Course rating: 4.3 out of 5.0 (323 Rating total)
• Duration: 1 Hour
• Certificate: Certificate on completion

## 10. Linear Algebra Refresher Course

Designed for students seeking a comprehensive review of linear algebra basics, this mini-course offers an opportunity to delve deeper into the significance and essence of linear algebra. Through the utilization of computer programs, participants will grasp key linear algebra concepts.

In this Linear Algebra course, you will learn the following:

• Vectors
• Intersections

By the course's conclusion, you will have developed a personal repertoire of linear algebra functions applicable to real-life scenarios, empowering you to confidently navigate practical situations.

• Duration: 4 Months
• Certificate: Certificate on completion

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