About this Course
29,059

100% 온라인

지금 바로 시작해 나만의 일정에 따라 학습을 진행하세요.

탄력적인 마감일

일정에 따라 마감일을 재설정합니다.

초급 단계

완료하는 데 약 12시간 필요

권장: 4 weeks of study, 3-4 hours/week...

영어

자막: 영어

100% 온라인

지금 바로 시작해 나만의 일정에 따라 학습을 진행하세요.

탄력적인 마감일

일정에 따라 마감일을 재설정합니다.

초급 단계

완료하는 데 약 12시간 필요

권장: 4 weeks of study, 3-4 hours/week...

영어

자막: 영어

강의 계획 - 이 강좌에서 배울 내용

1
완료하는 데 7시간 필요

MATRICES

In this week's lectures, we learn about matrices. Matrices are rectangular arrays of numbers or other mathematical objects and are fundamental to engineering mathematics. We will define matrices and how to add and multiply them, discuss some special matrices such as the identity and zero matrix, learn about transposes and inverses, and define orthogonal and permutation matrices. ...
11 videos (Total 84 min), 25 readings, 5 quizzes
11개의 동영상
Introduction1m
Definition of a Matrix7m
Addition and Multiplication of Matrices10m
Special Matrices9m
Transpose Matrix9m
Inner and Outer Products9m
Inverse Matrix12m
Orthogonal Matrices4m
Rotation Matrices8m
Permutation Matrices6m
25개의 읽기 자료
Welcome and Course Information5m
Get to Know Your Classmates10m
Practice: Construct Some Matrices10m
Practice: Matrix Addition and Multiplication10m
Practice: AB=AC Does Not Imply B=C10m
Practice: Matrix Multiplication Does Not Commute10m
Practice: Associative Law for Matrix Multiplication10m
Practice: AB=0 When A and B Are Not zero10m
Practice: Product of Diagonal Matrices10m
Practice: Product of Triangular Matrices10m
Practice: Transpose of a Matrix Product10m
Practice: Any Square Matrix Can Be Written as the Sum of a Symmetric and Skew-Symmetric Matrix10m
Practice: Construction of a Square Symmetric Matrix10m
Practice: Example of a Symmetric Matrix10m
Practice: Sum of the Squares of the Elements of a Matrix10m
Practice: Inverses of Two-by-Two Matrices10m
Practice: Inverse of a Matrix Product10m
Practice: Inverse of the Transpose Matrix10m
Practice: Uniqueness of the Inverse10m
Practice: Product of Orthogonal Matrices10m
Practice: The Identity Matrix is Orthogonal10m
Practice: Inverse of the Rotation Matrix10m
Practice: Three-dimensional Rotation10m
Practice: Three-by-Three Permutation Matrices10m
Practice: Inverses of Three-by-Three Permutation Matrices10m
5개 연습문제
Diagnostic Quiz10m
Matrix Definitions10m
Transposes and Inverses10m
Orthogonal Matrices10m
Week One30m
2
완료하는 데 3시간 필요

SYSTEMS OF LINEAR EQUATIONS

In this week's lectures, we learn about solving a system of linear equations. A system of linear equations can be written in matrix form, and we can solve using Gaussian elimination. We will learn how to bring a matrix to reduced row echelon form, and how this can be used to compute a matrix inverse. We will also learn how to find the LU decomposition of a matrix, and how to use this decomposition to efficiently solve a system of linear equations....
7 videos (Total 71 min), 6 readings, 3 quizzes
7개의 동영상
Gaussian Elimination14m
Reduced Row Echelon Form8m
Computing Inverses13m
Elementary Matrices11m
LU Decomposition10m
Solving (LU)x = b11m
6개의 읽기 자료
Practice: Gaussian Elimination10m
Practice: Reduced Row Echelon Form10m
Practice: Computing Inverses10m
Practice: Elementary Matrices10m
Practice: LU Decomposition10m
Practice: Solving (LU)x = b10m
3개 연습문제
Gaussian Elimination10m
LU Decomposition10m
Week Two30m
3
완료하는 데 6시간 필요

VECTOR SPACES

In this week's lectures, we learn about 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 will learn some of the vocabulary and phrases of linear algebra, such as linear independence, span, basis and dimension. We will 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....
13 videos (Total 140 min), 14 readings, 5 quizzes
13개의 동영상
Vector Spaces7m
Linear Independence9m
Span, Basis and Dimension10m
Gram-Schmidt Process13m
Gram-Schmidt Process Example9m
Null Space12m
Application of the Null Space14m
Column Space9m
Row Space, Left Null Space and Rank14m
Orthogonal Projections11m
The Least-Squares Problem10m
Solution of the Least-Squares Problem15m
14개의 읽기 자료
Practice: Zero Vector10m
Practice: Examples of Vector Spaces10m
Practice: Linear Independence10m
Practice: Orthonormal basis10m
Practice: Gram-Schmidt Process10m
Practice: Gram-Schmidt on Three-by-One Matrices10m
Practice: Gram-Schmidt on Four-by-One Matrices10m
Practice: Null Space10m
Practice: Underdetermined System of Linear Equations10m
Practice: Column Space10m
Practice: Fundamental Matrix Subspaces10m
Practice: Orthogonal Projections10m
Practice: Setting Up the Least-Squares Problem10m
Practice: Line of Best Fit10m
5개 연습문제
Vector Space Definitions10m
Gram-Schmidt Process10m
Fundamental Subspaces10m
Orthogonal Projections10m
Week Three30m
4
완료하는 데 6시간 필요

EIGENVALUES AND EIGENVECTORS

In this week's lectures, we will learn about determinants and the eigenvalue problem. We will learn how to compute determinants using a Laplace expansion, the Leibniz formula, or by row or column elimination. We will formulate the eigenvalue problem and learn how to find the eigenvalues and eigenvectors of a matrix. We will learn how to diagonalize a matrix using its eigenvalues and eigenvectors, and how this leads to an easy calculation of a matrix raised to a power. ...
13 videos (Total 120 min), 20 readings, 4 quizzes
13개의 동영상
Two-by-Two and Three-by-Three Determinants8m
Laplace Expansion13m
Leibniz Formula11m
Properties of a Determinant15m
The Eigenvalue Problem12m
Finding Eigenvalues and Eigenvectors (1)10m
Finding Eigenvalues and Eigenvectors (2)7m
Matrix Diagonalization9m
Matrix Diagonalization Example15m
Powers of a Matrix5m
Powers of a Matrix Example6m
Concluding Remarks3m
20개의 읽기 자료
Practice: Determinant of the Identity Matrix10m
Practice: Row Interchange10m
Practice: Determinant of a Matrix Product10m
Practice: Compute Determinant Using the Laplace Expansion10m
Practice: Compute Determinant Using the Leibniz Formula10m
Practice: Determinant of a Matrix With Two Equal Rows10m
Practice: Determinant is a Linear Function of Any Row10m
Practice: Determinant Can Be Computed Using Row Reduction10m
Practice: Compute Determinant Using Gaussian Elimination10m
Practice: Characteristic Equation for a Three-by-Three Matrix10m
Practice: Eigenvalues and Eigenvectors of a Two-by-Two Matrix10m
Practice: Eigenvalues and Eigenvectors of a Three-by-Three Matrix10m
Practice: Complex Eigenvalues10m
Practice: Linearly Independent Eigenvectors10m
Practice: Invertibility of the Eigenvector Matrix10m
Practice: Diagonalize a Three-by-Three Matrix10m
Practice: Matrix Exponential10m
Practice: Powers of a Matrix10m
Please Rate this Course10m
Acknowledgements1m
4개 연습문제
Determinants10m
The Eigenvalue Problem10m
Matrix Diagonalization10m
Week Four30m
4.8
40개의 리뷰Chevron Right

50%

이 강좌를 수료한 후 새로운 경력 시작하기

50%

이 강좌를 통해 확실한 경력상 이점 얻기

최상위 리뷰

대학: JMar 12th 2019

Es muy bueno el curso de verdad que lo recomiendo mucho para todos aquellos estudiantes que cursan Álgebra Lineal ya que tiene todas las herramientas necesarias para aprender esa materia

대학: RHNov 7th 2018

Very well-prepared and presented course on matrix/linear algebra operations, with emphasis on engineering considerations. Lecture notes with examples in PDF form are especially helpful.

강사

Avatar

Jeffrey R. Chasnov

Professor
Department of Mathematics

홍콩과학기술대학 정보

HKUST - A dynamic, international research university, in relentless pursuit of excellence, leading the advance of science and technology, and educating the new generation of front-runners for Asia and the world....

자주 묻는 질문

  • 강좌에 등록하면 바로 모든 비디오, 테스트 및 프로그래밍 과제(해당하는 경우)에 접근할 수 있습니다. 상호 첨삭 과제는 이 세션이 시작된 경우에만 제출하고 검토할 수 있습니다. 강좌를 구매하지 않고 살펴보기만 하면 특정 과제에 접근하지 못할 수 있습니다.

  • 수료증을 구매하면 성적 평가 과제를 포함한 모든 강좌 자료에 접근할 수 있습니다. 강좌를 완료하면 전자 수료증이 성취도 페이지에 추가되며, 해당 페이지에서 수료증을 인쇄하거나 LinkedIn 프로필에 수료증을 추가할 수 있습니다. 강좌 콘텐츠만 읽고 살펴보려면 해당 강좌를 무료로 청강할 수 있습니다.

궁금한 점이 더 있으신가요? 학습자 도움말 센터를 방문해 보세요.