Matrix Algebra for Engineers

Go to Course: https://www.coursera.org/learn/matrix-algebra-engineers

Introduction

**Course Review: Matrix Algebra for Engineers on Coursera** If you are an aspiring engineer or a professional looking to sharpen your skills in linear algebra, the course "Matrix Algebra for Engineers" on Coursera is an excellent starting point. This course is tailored to meet the specific needs of engineers, providing a concise yet comprehensive overview of matrix theory and its applications in engineering contexts. ### Overview "Matrix Algebra for Engineers" opens up the world of matrices, which are foundational in various engineering disciplines such as electrical, mechanical, and civil engineering. The course is designed for those who have completed a university-level single variable calculus course and possess a solid mathematical grounding. While it does not delve into derivatives or integrals, a basic level of mathematical maturity is expected. This makes it an ideal choice for advanced high school students, undergraduates, or anyone interested in brushing up on their linear algebra skills. ### Course Syllabus Breakdown 1. **Matrices:** The course begins with a foundational introduction to matrices. You'll learn how to define, add, and multiply matrices. The introduction to special matrices like the identity and zero matrices is particularly useful, as these concepts often arise in engineering applications. Additionally, the segments on transposition and inversion provide the tools necessary for advanced manipulation of matrices. 2. **Systems of Linear Equations:** Here, you'll encounter one of the most practical applications of matrices: solving systems of linear equations. The course covers Gaussian elimination and the reduced row echelon form, essential techniques for solving linear systems efficiently. You will also explore LU decomposition, which is invaluable for dealing with matrices that change over time. 3. **Vector Spaces:** The concept of vector spaces is explored in depth, introducing essential vocabulary like linear independence, span, basis, and dimension. Understanding these principles is crucial for any engineer, as they form the basis of many complex analyses. The chapter on least-squares problems demonstrates how to derive a line of best fit through noisy data, a common real-world challenge. 4. **Eigenvalues and Eigenvectors:** The final module tackles eigenvalues and eigenvectors, spotlighting their significance in matrix algebra. You will master the eigenvalue problem and learn various methods for calculating determinants. This portion of the course is particularly illuminating, as it shows how these concepts can simplify matrix calculations, including the powerful technique of diagonalization. ### Recommendation This course is highly recommended for anyone looking to understand the role of matrices in engineering. From professionals who need a refresher to students preparing for a career in engineering, "Matrix Algebra for Engineers" provides value for all. Its structured approach, combining theory with practical applications, ensures that learners not only digest the material but also apply it effectively. The instructors are knowledgeable and present the material in a clear and engaging manner. The course also includes quizzes and assignments that reinforce the learned concepts, making it a practical and interactive learning experience. ### Conclusion In summary, "Matrix Algebra for Engineers" on Coursera is a meticulously designed course that caters specifically to the needs of engineers. Its comprehensive syllabus covers the essential concepts of matrix algebra in an accessible format. If you are ready to dive into the world of matrices and enhance your engineering skills, this course is an excellent investment in your education and career.

Syllabus

MATRICES

Matrices are rectangular arrays of numbers, symbols, or expressions, arranged in rows and columns. We define matrices and show how to add and multiply them, define some special matrices such as the identity matrix and the zero matrix, learn about the transpose and inverse of a matrix, and discuss orthogonal and permutation matrices.

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, which can be used to compute the matrix inverse. We also learn how to find the LU decomposition of a matrix, and how this decomposition can be used to efficiently solve a system of linear equations with changing right-hand sides.

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.

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, and by row or column elimination. We also learn how to diagonalize a matrix using its eigenvalues and eigenvectors, and how this can be used to easily calculate a matrix raised to a power.