課程信息
4.8
27 個評分
7 個審閱
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初級

初級

完成時間(小時)

完成時間大約為13 小時

建議:4 weeks of study, 3-4 hours/week...
可選語言

英語(English)

字幕:英語(English)...
100% 在線

100% 在線

立即開始,按照自己的計劃學習。
可靈活調整截止日期

可靈活調整截止日期

根據您的日程表重置截止日期。
初級

初級

完成時間(小時)

完成時間大約為13 小時

建議:4 weeks of study, 3-4 hours/week...
可選語言

英語(English)

字幕:英語(English)...

教學大綱 - 您將從這門課程中學到什麼

1
完成時間(小時)
完成時間為 7 小時

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. ...
Reading
11 個視頻(共 84 分鐘), 24 個閱讀材料, 5 個測驗
Video11 個視頻
Introduction1分鐘
Definition of a Matrix7分鐘
Addition and Multiplication of Matrices10分鐘
Special Matrices9分鐘
Transpose Matrix9分鐘
Inner and Outer Products9分鐘
Inverse Matrix12分鐘
Orthogonal Matrices4分鐘
Orthogonal Matrices Example8分鐘
Permutation Matrices6分鐘
Reading24 個閱讀材料
Welcome and Course Information5分鐘
Get to Know Your Classmates10分鐘
Practice: Construct Some Matrices10分鐘
Practice: Matrix Addition and Multiplication10分鐘
Practice: AB=AC Does Not Imply B=C10分鐘
Practice: Matrix Multiplication Does Not Commute10分鐘
Practice: AB=0 When A and B Are Not zero10分鐘
Practice: Product of Diagonal Matrices10分鐘
Practice: Product of Triangular Matrices10分鐘
Practice: Transpose of a Matrix Product10分鐘
Practice: Any Square Matrix Can Be Written as the Sum of a Symmetric and Skew-Symmetric Matrix10分鐘
Practice: Construction of a Square Symmetric Matrix10分鐘
Practice: Example of a Symmetric Matrix10分鐘
Practice: Sum of the Squares of the Elements of a Matrix10分鐘
Practice: Inverses of Two-by-Two Matrices10分鐘
Practice: Inverse of a Matrix Product10分鐘
Practice: Inverse of the Transpose Matrix10分鐘
Practice: Uniqueness of the Inverse10分鐘
Practice: Product of Orthogonal Matrices10分鐘
Practice: The Identity Matrix is Orthogonal10分鐘
Practice: Inverse of the Rotation Matrix10分鐘
Practice: Three-dimensional Rotation10分鐘
Practice: Three-by-Three Permutation Matrices10分鐘
Practice: Inverses of Three-by-Three Permutation Matrices10分鐘
Quiz5 個練習
Diagnostic Quiz10分鐘
Matrix Definitions10分鐘
Transposes and Inverses10分鐘
Orthogonal Matrices10分鐘
Week One30分鐘
2
完成時間(小時)
完成時間為 3 小時

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....
Reading
7 個視頻(共 71 分鐘), 6 個閱讀材料, 3 個測驗
Video7 個視頻
Gaussian Elimination14分鐘
Reduced Row Echelon Form8分鐘
Computing Inverses13分鐘
Elementary Matrices11分鐘
LU Decomposition10分鐘
Solving (LU)x = b11分鐘
Reading6 個閱讀材料
Practice: Gaussian Elimination10分鐘
Practice: Reduced Row Echelon Form10分鐘
Practice: Computing Inverses10分鐘
Practice: Elementary Matrices10分鐘
Practice: LU Decomposition10分鐘
Practice: Solving (LU)x = b10分鐘
Quiz3 個練習
Gaussian Elimination10分鐘
LU Decomposition10分鐘
Week Two30分鐘
3
完成時間(小時)
完成時間為 6 小時

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....
Reading
13 個視頻(共 140 分鐘), 14 個閱讀材料, 5 個測驗
Video13 個視頻
Vector Spaces7分鐘
Linear Independence9分鐘
Span, Basis and Dimension10分鐘
Gram-Schmidt Process13分鐘
Gram-Schmidt Process Example9分鐘
Null Space12分鐘
Application of the Null Space14分鐘
Column Space9分鐘
Row Space, Left Null Space and Rank14分鐘
Orthogonal Projections11分鐘
The Least-Squares Problem10分鐘
Solution of the Least-Squares Problem15分鐘
Reading14 個閱讀材料
Practice: Zero Vector10分鐘
Practice: Examples of Vector Spaces10分鐘
Practice: Linear Independence10分鐘
Practice: Orthonormal basis10分鐘
Practice: Gram-Schmidt Process10分鐘
Practice: Gram-Schmidt on Three-by-One Matrices10分鐘
Practice: Gram-Schmidt on Four-by-One Matrices10分鐘
Practice: Null Space10分鐘
Practice: Underdetermined System of Linear Equations10分鐘
Practice: Column Space10分鐘
Practice: Fundamental Matrix Subspaces10分鐘
Practice: Orthogonal Projections10分鐘
Practice: Setting Up the Least-Squares Problem10分鐘
Practice: Line of Best Fit10分鐘
Quiz5 個練習
Vector Space Definitions10分鐘
Gram-Schmidt Process10分鐘
Fundamental Subspaces10分鐘
Orthogonal Projections10分鐘
Week Three30分鐘
4
完成時間(小時)
完成時間為 6 小時

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. ...
Reading
13 個視頻(共 120 分鐘), 20 個閱讀材料, 4 個測驗
Video13 個視頻
Two-by-Two and Three-by-Three Determinants8分鐘
Laplace Expansion13分鐘
Leibniz Formula11分鐘
Properties of a Determinant15分鐘
The Eigenvalue Problem12分鐘
Finding Eigenvalues and Eigenvectors (1)10分鐘
Finding Eigenvalues and Eigenvectors (2)7分鐘
Matrix Diagonalization9分鐘
Matrix Diagonalization Example15分鐘
Powers of a Matrix5分鐘
Powers of a Matrix Example6分鐘
Concluding Remarks3分鐘
Reading20 個閱讀材料
Practice: Determinant of the Identity Matrix10分鐘
Practice: Row Interchange10分鐘
Practice: Determinant of a Matrix Product10分鐘
Practice: Compute Determinant Using the Laplace Expansion10分鐘
Practice: Compute Determinant Using the Leibniz Formula10分鐘
Practice: Determinant of a Matrix With Two Equal Rows10分鐘
Practice: Determinant is a Linear Function of Any Row10分鐘
Practice: Determinant Can Be Computed Using Row Reduction10分鐘
Practice: Compute Determinant Using Gaussian Elimination10分鐘
Practice: Characteristic Equation for a Three-by-Three Matrix10分鐘
Practice: Eigenvalues and Eigenvectors of a Two-by-Two Matrix10分鐘
Practice: Eigenvalues and Eigenvectors of a Three-by-Three Matrix10分鐘
Practice: Complex Eigenvalues10分鐘
Practice: Linearly Independent Eigenvectors10分鐘
Practice: Invertibility of the Eigenvector Matrix10分鐘
Practice: Diagonalize a Three-by-Three Matrix10分鐘
Practice: Matrix Exponential10分鐘
Practice: Powers of a Matrix10分鐘
Please Rate this Course10分鐘
Acknowledgements1分鐘
Quiz4 個練習
Determinants10分鐘
The Eigenvalue Problem10分鐘
Matrix Diagonalization10分鐘
Week Four30分鐘
4.8
7 個審閱Chevron Right

熱門審閱

創建者 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.

講師

Avatar

Jeffrey R. Chasnov

Professor
Department of Mathematics

關於 The Hong Kong University of Science and Technology

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....

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