Matrix Algebra for Engineers
All-Time Top 100The Hong Kong University of Science and Technology via Coursera
- Provider Coursera
- Cost Free Online Course (Audit)
- Session In progress
- Language English
- Certificate Paid Certificate Available
- Effort 3-4 hours a week
- Duration 4 weeks long
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Overview
Class Central Tips
After each video, there are problems to solve and I have tried to choose problems that exemplify the main idea of the lecture. I try to give enough problems for students to solidify their understanding of the material, but not so many that students feel overwhelmed. I do encourage students to attempt the given problems, but if they get stuck, full solutions can be found in my lecture notes.
The mathematics in this matrix algebra course is presented at the level of an advanced high school student, but typically students would take this course after completing a university-level single variable calculus course. There are no derivatives or integrals in this course, but student's are expected to have a certain level of mathematical maturity. Nevertheless, anyone who wants to learn the basics of matrix algebra is welcome to join.
Lecture notes may be downloaded at
http://www.math.ust.hk/~machas/matrix-algebra-for-engineers.pdf
Watch the course overview video at
https://youtu.be/IZcyZHomFQc
Syllabus
-Matrices are rectangular arrays of numbers or other mathematical objects. We 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.
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, and how this can be used to compute a matrix inverse. We learn how to find the LU decomposition of a matrix, and how to use this decomposition to efficiently solve a system of linear equations with evolving 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
-We learn about determinants and the eigenvalue problem. We learn how to compute determinants using a Laplace expansion, the Leibniz formula, or by row or column elimination. We formulate the eigenvalue problem and learn how to find the eigenvalues and eigenvectors of a matrix. We 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.
Taught by
Class Central Charts
- #3 in Subjects / Mathematics
- #2 in Subjects / Engineering
- #1 in Subjects / Mathematics / Algebra & Geometry
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Reviews for Coursera's Matrix Algebra for Engineers Based on 53 reviews
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Did you take this course? Share your experience with other students.
Write a review- 1
Recommended to all!
videos are understanding and are very useful. I have learnt a lot from the course.
This course covers most of the important material for applications to differential equations, physics, computer science, economics, etc. Jeff Chasnov does keeps the lessons very tangible, and almost completely avoids abstraction altogether. I highly recommend the course. Even if you have taken an abstract linear algebra course, this is a good way to learn how to apply matrix algebra to real life.
We see how powerful matrices can be and, sometimes, in which concrete case can they be used.
Thus, from abstraction to application, I learned fundamental concept such as eingenvectors, Subspace of matrices, Gram-Schmidt process, LU decomposition etc.
The exercises help to better understand and assimilate the lectures.
The professor teaches very clearly, enthusiastically and answer quickly to the questions.
I strongly recommend this course to people who have, at least, a high school level in mathematics and want to get a full introduction in Matrix Algebra.
The first, the educator was very clear and the presentation technique through the use of a window board was
excellent. The educator's hands on approach through exposition and examples is to be commended.
The second the material is presented in a fashion that was not simple but not too hard to grasp given
effort. The reinforcement through the use of quizzes, with solved examples, and examination though
the use of tests, without solved examples, works.
The Third, the excellent text accompanying the course is first class.
This is a high quality course.
During I taking this course I built study site in Korean.
http://math-mass-goodkook.blogspot.com/search/label/%EC%9D%B4%EA%B3%BC%EC%83%9D%EC%9D%84+%EC%9C%84%ED%95%9C+%ED%96%89%EB%A0%AC+%EB%8C%80%EC%88%98
Thanks Prof. Chasnov for providing great course.
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