This course provides an overview of bachelor-level linear algebra. You will review all the concepts and practice and refresh the skills related to matrices and linear transformations. A strong foundation in mathematics is critical for success in all science and engineering disciplines. Whether you want to make a strong start to a master’s degree, prepare for more advanced courses, solidify your knowledge in a professional context or simply brush up on fundamentals, this course will get you up to speed.
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In many engineering master’s programs, you need to be familiar with linear algebra. This course will enable you to review the relevant topics.
This course focuses on matrices and linear transformations. Topics covered include matrix algebra, determinants, eigenvalues and eigenvectors, diagonalization and singular value decomposition. The course will help you refresh your knowledge, test your skills and review the relations between the many concepts in linear algebra.
The linear algebra courses within this series will offer you an overview of this branch of mathematics common to most engineering bachelor’s programs. They provide enough depth to cover the linear algebra you need to succeed in your engineering master’s/profession in areas such as computer graphics, systems and control, machine learning, quantum computing and more.
This is a review course
This self-contained course is modular, so you do not need to follow the entire course if you wish to focus on a particular aspect. As a review course you are expected to have previously studied or be familiar with most of the material. Hence the pace will be higher than in an introductory course.
This format is ideal for refreshing your bachelor level mathematics and letting you practice as much as you want. Through the Grasple platform, you will have access to plenty of exercises – often with different numbers – and receive intelligent, personal and immediate feedback.
This course is part of the Mastering Linear Algebra Professional Certificate.
Prerequisites:
Prior knowledge of all the material covered.
This is a self-contained bachelor-level course. However, we do assume that you are familiar with standard high school mathematics, specifically standard functions and their properties, algebraic manipulation of equations and inequalities and standard mathematical notation.
This course is a review course. As such the course requires you to have studied linear algebra in the past or at least to be familiar with its course contents. If this is not the case for you, then you can still do the course, but be prepared for a high pace!
What you'll learn
- Perform algebraic operations on matrices such as matrix multiplication and matrix inversion.
- Recognize linear transformations, apply their properties and find the standard matrix.
- Find the determinant of a matrix and apply properties of determinants in the context of algebra and geometry.
- Find eigenvalues, eigenvectors and eigenspaces of a matrix.
- Diagonalize a matrix if possible and perform other similarity transformations.
- Apply properties of symmetric matrices.
- Find the singular value decomposition of a matrix.
Syllabus
Week 1:
- matrix multiplication and addition
- matrix inversion
Week 2:
- linear transformations
- standard matrix of a linear transformation
- examples of linear transformations in geometry
Week 3:
- determinants
- methods to find determinants
- applications of determinants
Week 4:
- eigenvalues and eigenvectors
- eigenspaces
- characteristic polynomials
- complex eigenvalues
- multiplicities of eigenvalues
Week 5:
- diagonalization
- similarity transformations
- coordinate transformations
Week 6:
- symmetric matrices
- quadratic forms
- singular value decomposition
