Course Summary
Learn how to use matrix algebra for engineering applications in this comprehensive course. Gain practical skills that can be applied to real-world problems.Key Learning Points
- Understand the fundamentals of matrix algebra and its applications in engineering
- Learn to solve complex engineering problems using matrix algebra
- Develop practical skills that can be applied to real-world situations
Related Topics for further study
Learning Outcomes
- Understand the fundamentals of matrix algebra and its applications in engineering
- Develop the ability to solve complex engineering problems using matrix algebra
- Gain practical skills that can be applied to real-world situations
Prerequisites or good to have knowledge before taking this course
- Basic algebra knowledge
- Familiarity with engineering principles
Course Difficulty Level
IntermediateCourse Format
- Online
- Self-paced
- Video lectures
Similar Courses
- Advanced Linear Algebra for Engineers
- Numerical Methods for Engineers
Related Education Paths
- Mechanical Engineering Certification
- Electrical Engineering Certification
- Computer Science Certification
Notable People in This Field
- Gilbert Strang
- Stephen Boyd
Related Books
Description
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 typically students should take this course after completing a university-level single variable calculus course. There are no derivatives or integrals in this course, but students are expected to have attained a sufficient level of mathematical maturity. Nevertheless, anyone who wants to learn the basics of matrix algebra is welcome to join.
Knowledge
- Matrices
- Systems of Linear Equations
- Vector Spaces
- Eigenvalues and eigenvectors
Outline
- MATRICES
- Promotional Video
- Week One Introduction
- Definition of a Matrix | Lecture 1
- Addition and Multiplication of Matrices | Lecture 2
- Special Matrices | Lecture 3
- Transpose Matrix | Lecture 4
- Inner and Outer Products | Lecture 5
- Inverse Matrix | Lecture 6
- Orthogonal Matrices | Lecture 7
- Rotation Matrices | Lecture 8
- Permutation Matrices | Lecture 9
- Welcome and Course Information
- How to Write Math in the Discussions Using MathJax
- Construct Some Matrices
- Matrix Addition and Multiplication
- AB=AC Does Not Imply B=C
- Matrix Multiplication Does Not Commute
- Associative Law for Matrix Multiplication
- AB=0 When A and B Are Not zero
- Product of Diagonal Matrices
- Product of Triangular Matrices
- Transpose of a Matrix Product
- Any Square Matrix Can Be Written as the Sum of a Symmetric and Skew-Symmetric Matrix
- Construction of a Square Symmetric Matrix
- Example of a Symmetric Matrix
- Sum of the Squares of the Elements of a Matrix
- Inverses of Two-by-Two Matrices
- Inverse of a Matrix Product
- Inverse of the Transpose Matrix
- Uniqueness of the Inverse
- Product of Orthogonal Matrices
- The Identity Matrix is Orthogonal
- Inverse of the Rotation Matrix
- Three-dimensional Rotation
- Three-by-Three Permutation Matrices
- Inverses of Three-by-Three Permutation Matrices
- Diagnostic Quiz
- Matrix Definitions
- Transposes and Inverses
- Orthogonal Matrices
- Week One Assessment
- SYSTEMS OF LINEAR EQUATIONS
- Week Two Introduction
- Gaussian Elimination | Lecture 10
- Reduced Row Echelon Form | Lecture 11
- Computing Inverses | Lecture 12
- Elementary Matrices | Lecture 13
- LU Decomposition | Lecture 14
- Solving (LU)x = b | Lecture 15
- Gaussian Elimination
- Reduced Row Echelon Form
- Computing Inverses
- Elementary Matrices
- LU Decomposition
- Solving (LU)x = b
- Gaussian Elimination
- LU Decomposition
- Week Two Assessment
- VECTOR SPACES
- Week Three Introduction
- Vector Spaces | Lecture 16
- Linear Independence | Lecture 17
- Span, Basis and Dimension | Lecture 18
- Gram-Schmidt Process | Lecture 19
- Gram-Schmidt Process Example | Lecture 20
- Null Space | Lecture 21
- Application of the Null Space | Lecture 22
- Column Space | Lecture 23
- Row Space, Left Null Space and Rank | Lecture 24
- Orthogonal Projections | Lecture 25
- The Least-Squares Problem | Lecture 26
- Solution of the Least-Squares Problem | Lecture 27
- Zero Vector
- Examples of Vector Spaces
- Linear Independence
- Orthonormal basis
- Gram-Schmidt Process
- Gram-Schmidt on Three-by-One Matrices
- Gram-Schmidt on Four-by-One Matrices
- Null Space
- Underdetermined System of Linear Equations
- Column Space
- Fundamental Matrix Subspaces
- Orthogonal Projections
- Setting Up the Least-Squares Problem
- Line of Best Fit
- Vector Space Definitions
- Gram-Schmidt Process
- Fundamental Subspaces
- Orthogonal Projections
- Week Three Assessment
- EIGENVALUES AND EIGENVECTORS
- Week Four Introduction
- Two-by-Two and Three-by-Three Determinants | Lecture 28
- Laplace Expansion | Lecture 29
- Leibniz Formula | Lecture 30
- Properties of a Determinant | Lecture 31
- The Eigenvalue Problem | Lecture 32
- Finding Eigenvalues and Eigenvectors (1) | Lecture 33
- Finding Eigenvalues and Eigenvectors (2) | Lecture 34
- Matrix Diagonalization | Lecture 35
- Matrix Diagonalization Example | Lecture 36
- Powers of a Matrix | Lecture 37
- Powers of a Matrix Example | Lecture 38
- Concluding Remarks
- Determinant of the Identity Matrix
- Row Interchange
- Determinant of a Matrix Product
- Compute Determinant Using the Laplace Expansion
- Compute Determinant Using the Leibniz Formula
- Determinant of a Matrix With Two Equal Rows
- Determinant is a Linear Function of Any Row
- Determinant Can Be Computed Using Row Reduction
- Compute Determinant Using Gaussian Elimination
- Characteristic Equation for a Three-by-Three Matrix
- Eigenvalues and Eigenvectors of a Two-by-Two Matrix
- Eigenvalues and Eigenvectors of a Three-by-Three Matrix
- Complex Eigenvalues
- Linearly Independent Eigenvectors
- Invertibility of the Eigenvector Matrix
- Diagonalize a Three-by-Three Matrix
- Matrix Exponential
- Powers of a Matrix
- Please Rate this Course
- Determinants
- The Eigenvalue Problem
- Matrix Diagonalization
- Week Four Assessment
Summary of User Reviews
Key Aspect Users Liked About This Course
Many users have praised the course for its practical applications, which help students understand the real-world uses of matrix algebra.Pros from User Reviews
- Clear explanations make it easy to understand complex concepts
- Practical applications help students see the value of matrix algebra in the real world
- Experienced instructors provide helpful feedback and guidance throughout the course
- Flexible scheduling and self-paced learning options make it easy to fit the course into a busy schedule
Cons from User Reviews
- Some users have found the course to be too basic for their needs
- A few reviewers have noted that the course can be repetitive at times
- Some students have found the homework assignments to be too difficult or time-consuming
- A few users have reported technical issues with the online platform
Jeffrey R. Chasnov
4.8 Raiting
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