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
The course contains 38 short lecture videos, with a few problems to solve after each lecture. And after each substantial topic, there is a short practice quiz. Solutions to the problems and practice quizzes can be found in instructor-provided lecture notes. There are a total of four weeks in the course, and at the end of each week there is an assessed quiz.
Lecture notes can be downloaded from
http://www.math.ust.hk/~machas/matrix-algebra-for-engineers.pdf
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
-An eigenvector of a matrix is a nonzero column vector that when multiplied by the matrix is only multiplied by a scalar, called the eigenvalue. We learn about the eigenvalue problem and how to use determinants to find the eigenvalues of a matrix. We learn how to compute determinants using the Laplace expansion, the Leibniz formula, or by row or column elimination. We also 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
- #1 in Subjects / Engineering
- #1 in Subjects / Mathematics / Algebra & Geometry
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Reviews for Coursera's Matrix Algebra for Engineers Based on 60 reviews
- 5 stars 88%
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Did you take this course? Share your experience with other students.
Write a review- 1
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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