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.
제공자:
이 강좌에 대하여
배울 내용
Matrices
Systems of Linear Equations
Vector Spaces
Eigenvalues and eigenvectors
제공자:

홍콩과학기술대학
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.
강의 계획표 - 이 강좌에서 배울 내용
MATRICES
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.
검토
- 5 stars88.26%
- 4 stars10.40%
- 3 stars0.98%
- 2 stars0.16%
- 1 star0.19%
MATRIX ALGEBRA FOR ENGINEERS의 최상위 리뷰
This is a carefully sequenced, content-rich introduction to Matrices; beware skimming over details: eg. the use of matrix formalism to solve the least squares problem is little short of magic.
Very good and straight-forward course. Very engineering-oriented (not many proofs). I had already learnt matrix algebra before so this was a good way to recall my previous knowledge.
It teaches quite a lot about the fundamentals of linear algebra. I do wish that there were more examples but maybe it also depends on the learner if they want to learn more problems.
Very informative and well organized. The faculty is very responsive when it comes to queries. This is the second course that I have taken by this faculty. Looking forward to more!
Mathematics for Engineers 특화 과정 정보
This specialization was developed for engineering students to self-study engineering mathematics. We expect students are already familiar with single variable calculus and computer programming. Students will learn matrix algebra, differential equations, vector calculus and numerical methods. MATLAB programming will be taught. Watch the promotional video!

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