This is the third and final course in the Linear Algebra Specialization that focuses on the theory and computations that arise from working with orthogonal vectors. This includes the study of orthogonal transformation, orthogonal bases, and orthogonal transformations. The course culminates in the theory of symmetric matrices, linking the algebraic properties with their corresponding geometric equivalences. These matrices arise more often in applications than any other class of matrices.
Linear Algebra: Orthogonality and Diagonalization
Give your career the gift of Coursera Plus with $160 off, billed annually. Save today.
Linear Algebra: Orthogonality and Diagonalization
This course is part of Linear Algebra from Elementary to Advanced Specialization
Instructor: Joseph W. Cutrone, PhD
Top Instructor
1,516 already enrolled
Included with 
Gain insight into a topic and learn the fundamentals.
4.9
(27 reviews)
Intermediate level
Some related experience required
9 hours to complete
3 weeks at 3 hours a week
Flexible schedule
Learn at your own pace
Details to know
Shareable certificate
Add to your LinkedIn profile
Assessments
11 assignments
Taught in English
See how employees at top companies are mastering in-demand skills
Build your subject-matter expertise
This course is part of the Linear Algebra from Elementary to Advanced Specialization
When you enroll in this course, you'll also be enrolled in this Specialization.
- Learn new concepts from industry experts
- Gain a foundational understanding of a subject or tool
- Develop job-relevant skills with hands-on projects
- Earn a shareable career certificate
Earn a career certificate
Add this credential to your LinkedIn profile, resume, or CV
Share it on social media and in your performance review
There are 4 modules in this course
In this module, we define a new operation on vectors called the dot product. This operation is a function that returns a scalar related to the angle between the vectors, distance between vectors, and length of vectors. After working through the theory and examples, we hone in on both unit (length one) and orthogonal (perpendicular) vectors. These special vectors will be pivotal in our course as we start to define linear transformations and special matrices that use only these vectors.
What's included
2 videos2 readings3 assignments
In this module we will study the special type of transformation called the orthogonal projection. We have already seen the formula for the orthogonal projection onto a line so now we generalize the formula to the case of projection onto any subspace W. The formula will require basis vectors that are both orthogonal and normalize and we show, using the Gram-Schmidt Process, how to meet these requirements given any non-empty basis.
What's included
3 videos3 readings4 assignments
In this module we look to diagonalize symmetric matrices. The symmetry displayed in the matrix A turns out to force a beautiful relationship between the eigenspaces. The corresponding eigenspaces turn out to be mutually orthogonal. After normalizing, these orthogonal eigenvectors give a very special basis of R^n with extremely useful applications to data science, machine learning, and image processing. We introduce the notion of quadratic forms, special functions of degree two on vectors , which use symmetric matrices in their definition. Quadratic forms are then completely classified based on the properties of their eigenvalues.
What's included
2 videos2 readings3 assignments
What's included
1 assignment
Instructor
Offered by
Recommended if you're interested in Machine Learning
Johns Hopkins University
Alberta Machine Intelligence Institute
EIT Digital
Korea Advanced Institute of Science and Technology(KAIST)
Why people choose Coursera for their career
Felipe M.
Learner since 2018
"To be able to take courses at my own pace and rhythm has been an amazing experience. I can learn whenever it fits my schedule and mood."
Jennifer J.
Learner since 2020
"I directly applied the concepts and skills I learned from my courses to an exciting new project at work."
Larry W.
Learner since 2021
"When I need courses on topics that my university doesn't offer, Coursera is one of the best places to go."
Chaitanya A.
"Learning isn't just about being better at your job: it's so much more than that. Coursera allows me to learn without limits."
Learner reviews
Showing 3 of 27
4.9
27 reviews
- 5 stars
92.59%
- 4 stars
7.40%
- 3 stars
0%
- 2 stars
0%
- 1 star
0%
MD
5
Reviewed on Nov 4, 2024
New to Machine Learning? Start here.
Open new doors with Coursera Plus
Unlimited access to 7,000+ world-class courses, hands-on projects, and job-ready certificate programs - all included in your subscription
Advance your career with an online degree
Earn a degree from world-class universities - 100% online
Join over 3,400 global companies that choose Coursera for Business
Upskill your employees to excel in the digital economy
Frequently asked questions
Access to lectures and assignments depends on your type of enrollment. If you take a course in audit mode, you will be able to see most course materials for free. To access graded assignments and to earn a Certificate, you will need to purchase the Certificate experience, during or after your audit. If you don't see the audit option:
The course may not offer an audit option. You can try a Free Trial instead, or apply for Financial Aid.
The course may offer 'Full Course, No Certificate' instead. This option lets you see all course materials, submit required assessments, and get a final grade. This also means that you will not be able to purchase a Certificate experience.
When you enroll in the course, you get access to all of the courses in the Specialization, and you earn a certificate when you complete the work. Your electronic Certificate will be added to your Accomplishments page - from there, you can print your Certificate or add it to your LinkedIn profile. If you only want to read and view the course content, you can audit the course for free.
If you subscribed, you get a 7-day free trial during which you can cancel at no penalty. After that, we don’t give refunds, but you can cancel your subscription at any time. See our full refund policy.