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Matrix Algebra for Engineers

This course is all about matrices, and concisely covers the linear algebra that an engineer should know. The mathematics in this course is presented at the level of an advanced high school student, but it is recommended that students take this course after completing a university-level single variable calculus course. There are no derivatives or integrals involved, but students are expected to have a basic level of mathematical maturity. Despite this, anyone interested in learning the basics of matrix algebra is welcome to join.

The course consists of 38 concise lecture videos, each followed by a few problems to solve. After each major topic, there is a short practice quiz. Solutions to the problems and practice quizzes can be found in the instructor-provided lecture notes. The course spans four weeks, and at the end of each week, there is an assessed quiz.

Download the lecture notes from the link

https://www.math.hkust.edu.hk/~machas/matrix-algebra-for-engineers.pdf

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https://youtu.be/IZcyZHomFQc

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What's inside

Syllabus

MATRICES

Matrices are rectangular arrays of numbers, symbols, or expressions, arranged in rows and columns. We define matrices and show how to add and multiply them, define some special matrices such as the identity matrix and the zero matrix, learn about the transpose and inverse of a matrix, and discuss orthogonal and permutation matrices.

SYSTEMS OF LINEAR EQUATIONS

A system of linear equations can be written in matrix form, and can be solved using Gaussian elimination. We learn how to bring a matrix to reduced row echelon form, which can be used to compute the matrix inverse. We also learn how to find the LU decomposition of a matrix, and how this decomposition can be used to efficiently solve a system of linear equations with changing right-hand sides.

VECTOR SPACES

A vector space consists of a set of vectors and a set of scalars that is closed under vector addition and scalar multiplication and that satisfies the usual rules of arithmetic. We learn some of the vocabulary and phrases of linear algebra, such as linear independence, span, basis and dimension. We learn about the four fundamental subspaces of a matrix, the Gram-Schmidt process, orthogonal projection, and the matrix formulation of the least-squares problem of drawing a straight line to fit noisy data.

EIGENVALUES AND EIGENVECTORS

An eigenvector of a matrix is a nonzero column vector that when multiplied by the matrix is only multiplied by a scalar (called the eigenvalue). We learn about the eigenvalue problem and how to use determinants to find the eigenvalues of a matrix. We learn how to compute determinants using the Laplace expansion, the Leibniz formula, and by row or column elimination. We also learn how to diagonalize a matrix using its eigenvalues and eigenvectors, and how this can be used to easily calculate a matrix raised to a power.

Good to know

Know what's good

, what to watch for

, and possible dealbreakers

Explores matrices, which is standard in engineering

Well-structured four-week program, with practice quizzes and assessed quizzes

Taught by Jeffrey R. Chasnov, who is recognized for their expertise in matrix algebra

Teaches skills, knowledge, and tools that are highly relevant to engineering

Suits learners with a variety of backgrounds, as it requires only basic mathematical maturity

Builds a strong foundation in matrix algebra for beginners

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Reviews summary

Matrix tools for stem

This Coursera course titled "Matrix Algebra for Engineers" teaches students how to use matrices to solve problems in engineering and other science and technology fields. Learners say the course is largely positive, with engaging assignments and a focus on practical applications. The course is well received by learners and to highlight key features and concepts, reviewers' comments have been bolded throughout the summary. They especially liked that the course is well paced and easy to understand, and also provides many exercises and challenging but not over the top quizzes. Many also commented that the course's lectures, readings, and exams were well organized and helped to strengthen their understanding of the material. Additionally, students said that the course covers most of the material that an engineer would need from Linear Algebra, including important concepts like Gaussian elimination, eigenvalues, and eigenvectors. Also great for beginners in matrix algebra, the course provides a concise and very helpful review with some methods introduced that are life-saving. Overall, learners say this course is largely positive with a great instructor who explains harder topics in an easy way and is able to create general rules for solving certain problems. One reviewer sums up their positive experience by saying: "This is one of the important courses in engineering, it is highly recommended especially for those who want to excel their potential in calculations."

- Vector spaces - Null space - Column space - Row space - Least squares problem

"This is an excellent course for engineers to begin with fundamental matrix algebra."

"The course is particularly clear and synthetic, but a little short."

"A very concise overview of the most important components of matrix algebra for engineers from all disciplines."

- Gaussian elimination - Eigenvalues - Eigenvectors

"There are a lot of things I learned in this course. I am familiar with the topics but I found myself in awe because I didn't know that I can understand how the formulas I've been memorizing this whole time are from!!"

"I took this course to pick up what I have learned before."

"This course help me to learn a lot of matrix knowledge."

- Well paced - Easy to understand - Provides many exercises - Challenging but not over the top quizzes - Well organized lectures, readings, and exams - Covers most of the material that an engineer would need from Linear Algebra - Great for beginners in matrix algebra - Provides a concise and very helpful review - Great instructor who explains harder topics in an easy way - Able to create general rules for solving certain problems

"It was a wonderful refresher of my fundamentals of Vector Algebra. The course is very well designed for online learning."

"This is such a great course. I have learned a lot."

"The course was generally easy to follow and the professor really made great length and effort to explain matrices and the it's application."

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 Matrix Algebra for Engineers with these activities:

Review prerequisites for matrix algebra

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Ensure a strong foundation in prerequisites to support successful learning in this course.

Browse courses on Calculus

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Review fundamental concepts from single variable calculus (e.g., limits, derivatives, integrals).
Refresh your understanding of basic linear algebra concepts (e.g., vectors, matrices, operations).

Review Strang's Introduction to Linear Algebra, 4th Edition by Gilbert Strang

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Provide a base knowledge of matrix algebra to ease the transition into the more advanced topics covered in the course.

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Read sections 1.1-1.2 in the book.
Complete practice problems 1.1-1.2.
Review the lecture notes from week 1 of the course.

Follow tutorials on QR decomposition

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Supplement the course material by exploring QR decomposition and its applications in linear algebra.

Browse courses on QR Decomposition

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Identify online tutorials or video lectures on QR decomposition.
Follow the tutorials, taking notes and working through the examples.
Apply the concepts learned to solve practice problems.

Three other activities

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Solve practice problems for Eigenvalues and Eigenvectors

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Reinforce the concepts of eigenvalues and eigenvectors, and gain proficiency in matrix diagonalization.

Browse courses on Eigenvalues

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Attempt the practice problems for Eigenvalues and Eigenvectors in the lecture notes.
Check your solutions against the answer key provided.
Explore additional practice problems from textbooks or online resources.

Create a tutorial on Gaussian elimination

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Develop a deeper understanding of Gaussian elimination and its applications in solving systems of linear equations.

Browse courses on Gaussian Elimination

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Review the concept of Gaussian elimination and its steps.
Create a video or written tutorial explaining the process clearly.
Provide examples to illustrate the method and its applications.

Implement a matrix library in Python

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Apply the concepts of matrix algebra to software development, reinforcing understanding and practicality.

Browse courses on Python Programming

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Choose a Python library or framework for matrix operations.
Define the classes and methods for matrix representation and operations.
Implement basic matrix operations (addition, subtraction, multiplication).
Extend the library with advanced operations (e.g., determinant, inverse).
Test and debug the library thoroughly.

Career center

Learners who complete Matrix Algebra for Engineers will develop knowledge and skills that may be useful to these careers:

Data Scientist

Data Scientists focus on analyzing data with a goal of extracting meaningful insights. These insights can be used to inform better decision-making, identify trends, and improve business outcomes. Matrix Algebra is an important skill for data scientists as it helps them to understand and manipulate data more effectively. For example, matrix algebra can be used to perform linear algebra operations such as matrix multiplication and solving systems of linear equations. These operations are essential for tasks such as data cleaning, feature engineering, and model building.

See salaries and explore the career path for Data Scientist

Financial Analyst

Financial analysts use mathematical and statistical techniques to evaluate and make recommendations on investments. They use matrix algebra to build financial models, which are used to forecast future financial performance and make investment decisions. Matrix algebra is also used to analyze financial data and to perform risk assessments.

See salaries and explore the career path for Financial Analyst

Operations Research Analyst

Operations research analysts use mathematical and analytical techniques to solve problems in business and industry. They use matrix algebra to build mathematical models that can be used to optimize processes, improve efficiency, and reduce costs. Matrix algebra is also used to analyze data and to make recommendations on how to improve business operations.

See salaries and explore the career path for Operations Research Analyst

Software Engineer

Software engineers design, develop, and maintain software systems. They use matrix algebra to solve problems in computer graphics, image processing, and machine learning. Matrix algebra is also used to optimize code and to improve the performance of software systems.

See salaries and explore the career path for Software Engineer

Actuary

Actuaries use mathematical and statistical techniques to assess risk and uncertainty. They use matrix algebra to build financial models that can be used to calculate insurance premiums, pensions, and other financial products. Matrix algebra is also used to analyze data and to make recommendations on how to manage risk.

See salaries and explore the career path for Actuary

Statistician

Statisticians use mathematical and statistical techniques to collect, analyze, and interpret data. They use matrix algebra to build statistical models that can be used to make predictions, draw inferences, and test hypotheses. Matrix algebra is also used to analyze data and to develop new statistical methods.

See salaries and explore the career path for Statistician

Quantitative Analyst

Quantitative analysts use mathematical and statistical techniques to analyze financial data and make investment decisions. They use matrix algebra to build financial models that can be used to forecast future financial performance and make investment decisions. Matrix algebra is also used to analyze financial data and to perform risk assessments.

See salaries and explore the career path for Quantitative Analyst

Risk Analyst

Risk analysts use mathematical and statistical techniques to assess risk and uncertainty. They use matrix algebra to build financial models that can be used to calculate insurance premiums, pensions, and other financial products. Matrix algebra is also used to analyze data and to make recommendations on how to manage risk.

See salaries and explore the career path for Risk Analyst

Data Analyst

Data analysts use mathematical and statistical techniques to analyze data and extract meaningful insights. They use matrix algebra to build statistical models that can be used to make predictions, draw inferences, and test hypotheses. Matrix algebra is also used to analyze data and to develop new statistical methods.

See salaries and explore the career path for Data Analyst

Actuary Assistant

Actuarial Assistants assist actuaries with a variety of tasks, including data analysis, model building, and risk assessment. Matrix algebra is essential for these tasks, as it allows actuarial assistants to perform complex mathematical operations efficiently. For example, matrix algebra can be used to solve systems of linear equations, which is a common task in actuarial work.

See salaries and explore the career path for Actuary Assistant

Business Analyst

Business analysts use mathematical and statistical techniques to analyze business data and make recommendations on how to improve business performance. Matrix algebra is a valuable tool for business analysts, as it allows them to perform complex mathematical operations efficiently. For example, matrix algebra can be used to solve systems of linear equations, which is a common task in business analysis.

See salaries and explore the career path for Business Analyst

Data Engineer

Data engineers design, build, and maintain data pipelines. They use matrix algebra to transform and clean data, as well as to build data models. Matrix algebra is also used to design and optimize data storage systems.

See salaries and explore the career path for Data Engineer

Financial Risk Manager

Financial risk managers use mathematical and statistical techniques to assess and manage risk in financial institutions. Matrix algebra is essential for this role, as it allows financial risk managers to perform complex mathematical operations efficiently. For example, matrix algebra can be used to solve systems of linear equations, which is a common task in financial risk management.

See salaries and explore the career path for Financial Risk Manager

Operations Analyst

Operations analysts use mathematical and statistical techniques to analyze and improve business operations. Matrix algebra is a valuable tool for operations analysts, as it allows them to perform complex mathematical operations efficiently. For example, matrix algebra can be used to solve systems of linear equations, which is a common task in operations analysis.

See salaries and explore the career path for Operations Analyst

Research Analyst

Research analysts use mathematical and statistical techniques to analyze data and make recommendations on investment decisions. Matrix algebra is a valuable tool for research analysts, as it allows them to perform complex mathematical operations efficiently. For example, matrix algebra can be used to solve systems of linear equations, which is a common task in investment research.

See salaries and explore the career path for Research Analyst

Reading list

We've selected 11 books that we think will supplement your learning. Use these to develop background knowledge, enrich your coursework, and gain a deeper understanding of the topics covered in Matrix Algebra for Engineers.

Matrix Analysis

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This textbook comprehensive treatment of matrix analysis. It covers all the essential topics, as well as some more advanced topics such as singular value decomposition and matrix norms. It is written in a clear and concise style, and it includes numerous examples and exercises.

Matrix Analysis

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Matrix Algebra for Engineers

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What's inside

Syllabus

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Reviews summary

Matrix tools for stem

Activities

Career center

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