К содержимому
learnspaceYOUR NEXT CHAPTER
ПРОСТРАНСТВО ОБУЧЕНИЯ
ГлавнаяКаталог курсовМоё обучениеCoursera

Знания без границ

Учитесь у лучших университетов и компаний мира.

Открыть Coursera
Интеграция
Пространство университета
Моё пространствоСтраница курса
↵
ЯЛичный кабинетСтудент
© 2026 LearnSpaceКаждый день — возможность узнать больше.Помощь
Matrix Algebra for Engineers · LearnSpace
Назад в каталог
courseraМатематика

Matrix Algebra for Engineers

Курс от The Hong Kong University of Science and Technology
Начальный≈ 19.6 чАнглийский
О курсеНавыкиПрограммаПреподаватели

О курсе

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, such as the Coursera offering Calculus for Engineers. 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 And watch the promotional video from the link https://youtu.be/IZcyZHomFQc

Навыки, которые вы освоите

Linear AlgebraAlgebraEngineering CalculationsApplied MathematicsGeneral MathematicsEngineering AnalysisNumerical AnalysisAdvanced Mathematics

Программа курса

4 модулей · 127 учебных материалов

01MATRICES41 материалов

Welcome to Matrix Algebra for Engineers

Welcome and Course InformationЧтениеDiagnostic Quiz ЗаданиеHow to Write Math in the Discussion Forums Using MathJaxЧтение

Introduction to Week One

Week One Introduction

Учитесь у экспертов

Jeffrey R. Chasnov

Professor

Matrix Algebra for Engineers
В каталоге вашей программы

Инвестируйте в себя

Новые знания — в удобное для вас время.

Начать на Coursera

Обучение откроется на Coursera
в новой вкладке

Обучение на Coursera

≈ 19.6 ч

4 модулей

Язык: Английский

Субтитры: Арабский, Французский, Бенгальский, Узбекский, Украинский, Китайский (Китай), Греческий, Итальянский, Бразильский португальский, Вьетнамский, Нидерландский, Корейский, Немецкий, Пушту, Урду, Русский, Тайский, Индонезийский, Шведский, Турецкий, Азербайджанский, Испанский, Дари, Хинди, Японский, Казахский, Венгерский, Польский

Часть программы вашего университета
Видео

Matrix Definitions

Definition of a Matrix | Lecture 1ВидеоConstruct Some MatricesЧтениеAddition and Multiplication of Matrices | Lecture 2ВидеоMatrix Addition and MultiplicationЧтениеAB=AC Does Not Imply B=CЧтениеMatrix Multiplication Does Not CommuteЧтениеAssociative Law for Matrix MultiplicationЧтениеSpecial Matrices | Lecture 3ВидеоAB=0 When A and B Are Not zeroЧтениеProduct of Diagonal MatricesЧтениеProduct of Triangular MatricesЧтениеMatrix Definitions Задание

Transpose and Inverses

Transpose Matrix | Lecture 4ВидеоTranspose of a Matrix ProductЧтениеAny Square Matrix Can Be Written as the Sum of a Symmetric and Skew-Symmetric MatrixЧтениеConstruction of a Square Symmetric MatrixЧтениеInner and Outer Products | Lecture 5ВидеоExample of a Symmetric MatrixЧтениеSum of the Squares of the Elements of a MatrixЧтениеInverse Matrix | Lecture 6ВидеоInverses of Two-by-Two MatricesЧтениеInverse of a Matrix ProductЧтениеInverse of the Transpose MatrixЧтениеUniqueness of the InverseЧтениеDeterminant as an AreaЧтениеTransposes and InversesЗадание

Orthogonal Matrices

Orthogonal Matrices | Lecture 7ВидеоProduct of Orthogonal MatricesЧтениеThe Identity Matrix is OrthogonalЧтениеRotation Matrices | Lecture 8ВидеоInverse of the Rotation MatrixЧтениеThree-dimensional RotationЧтениеPermutation Matrices | Lecture 9ВидеоThree-by-Three Permutation MatricesЧтениеInverses of Three-by-Three Permutation MatricesЧтениеOrthogonal MatricesЗадание

Quiz

Week One AssessmentЗадание
02SYSTEMS OF LINEAR EQUATIONS16 материалов

Introduction to Week Two

Week Two IntroductionВидео

Gaussian Elimination

Gaussian Elimination | Lecture 10ВидеоGaussian EliminationЧтениеReduced Row Echelon Form | Lecture 11ВидеоReduced Row Echelon FormЧтениеComputing Inverses | Lecture 12ВидеоComputing InversesЧтениеGaussian Elimination Задание

LU Decomposition

Elementary Matrices | Lecture 13ВидеоElementary MatricesЧтениеLU Decomposition | Lecture 14ВидеоLU DecompositionЧтениеSolving (LU)x = b | Lecture 15ВидеоSolving (LU)x = bЧтениеLU Decomposition

Quiz

Week Two Assessment Задание
03VECTOR SPACES32 материалов

Introduction to Week Three

Week Three IntroductionВидео

Vector Space Definitions

Vector Spaces | Lecture 16ВидеоZero VectorЧтениеExamples of Vector SpacesЧтениеLinear Independence | Lecture 17ВидеоLinear IndependenceЧтениеSpan, Basis and Dimension | Lecture 18ВидеоOrthonormal basisЧтениеVector Space DefinitionsЗадание

Gram-Schmidt process

Gram-Schmidt Process | Lecture 19ВидеоGram-Schmidt ProcessЧтениеGram-Schmidt Process Example | Lecture 20ВидеоGram-Schmidt on Three-by-One MatricesЧтениеGram-Schmidt on Four-by-One MatricesЧтениеGram-Schmidt Process Задание

Fundamental Subspaces of a Matrix

Null Space | Lecture 21ВидеоNull SpaceЧтениеApplication of the Null Space | Lecture 22ВидеоUnderdetermined System of Linear EquationsЧтениеColumn Space | Lecture 23ВидеоColumn SpaceЧтение

Orthogonal Projections

Orthogonal Projections | Lecture 25ВидеоOrthogonal ProjectionsЧтениеThe Least-Squares Problem | Lecture 26ВидеоSetting Up the Least-Squares ProblemЧтениеSolution of the Least-Squares Problem | Lecture 27ВидеоLine of Best FitЧтение

Quiz

Week Three AssessmentЗадание
04EIGENVALUES AND EIGENVECTORS38 материалов

Introduction to Week Four

Week Four IntroductionВидео

Determinants

Two-by-Two and Three-by-Three Determinants | Lecture 28ВидеоDeterminant of the Identity MatrixЧтениеRow InterchangeЧтениеDeterminant of a Matrix ProductЧтениеLaplace Expansion | Lecture 29ВидеоCompute Determinant Using the Laplace ExpansionЧтениеLeibniz Formula | Lecture 30ВидеоCompute Determinant Using the Leibniz FormulaЧтениеProperties of a Determinant | Lecture 31ВидеоDeterminant of a Matrix With Two Equal RowsЧтениеDeterminant is a Linear Function of Any RowЧтениеDeterminant Can Be Computed Using Row ReductionЧтениеCompute Determinant Using Gaussian EliminationЧтениеDeterminants ЗаданиеDeep Dive into How to Derive Cramer's RulePLUGIN

The Eigenvalue Problem

The Eigenvalue Problem | Lecture 32ВидеоCharacteristic Equation for a Three-by-Three MatrixЧтениеFinding Eigenvalues and Eigenvectors (Part A) | Lecture 33ВидеоEigenvalues and Eigenvectors of a Two-by-Two MatrixЧтениеEigenvalues and Eigenvectors of a Three-by-Three MatrixЧтениеFinding Eigenvalues and Eigenvectors (Part B) | Lecture 34Видео

Matrix Diagonalization

Matrix Diagonalization | Lecture 35ВидеоLinearly Independent EigenvectorsЧтениеInvertibility of the Eigenvector MatrixЧтениеMatrix Diagonalization Example | Lecture 36ВидеоDiagonalize a Three-by-Three MatrixЧтениеPowers of a Matrix | Lecture 37Видео

Quiz

Week Four Assessment Задание

Farewell

Concluding RemarksВидеоPlease Rate this CourseЧтениеAcknowledgementsЧтение
Задание
Row Space, Left Null Space and Rank | Lecture 24Видео
Fundamental Matrix SubspacesЧтение
Fundamental Subspaces Задание
Orthogonal Projections Задание
Complex EigenvaluesЧтение
The Eigenvalue Problem Задание
Matrix ExponentialЧтение
Powers of a Matrix Example | Lecture 38Видео
Powers of a MatrixЧтение
Matrix Diagonalization Задание