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 it is recommended that students take this course after completing a university-level single variable calculus course. There are no derivatives or integrals involved, but students are expected to have a basic level of mathematical maturity. Despite this, anyone interested in learning the basics of matrix algebra is welcome to join.

# Matrix Algebra for Engineers

This course is part of Mathematics for Engineers Specialization

Taught in English

Some content may not be translated

Instructor: Jeffrey R. Chasnov

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## Course

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## What you'll learn

Matrices

Systems of Linear Equations

Vector Spaces

Eigenvalues and eigenvectors

## Details to know

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21 quizzes

## Course

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## There are 4 modules in this course

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.

#### What's included

10 videos27 readings6 quizzes

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.

#### What's included

7 videos6 readings4 quizzes

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.

#### What's included

13 videos14 readings6 quizzes

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.

#### What's included

13 videos20 readings5 quizzes

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The Hong Kong University of Science and Technology

The Hong Kong University of Science and Technology

The Hong Kong University of Science and Technology

The Hong Kong University of Science and Technology

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## Frequently asked questions

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