Linear Algebra: Orthogonality and Diagonalization
This course is part of Linear Algebra from Elementary to Advanced.
This course cannot be purchased separately - to access the complete learning experience, graded assignments, and earn certificates, you'll need to enroll in the full Linear Algebra from Elementary to Advanced Specialization program. You can audit this specific course for free to explore the content, which includes access to course materials and lectures. This allows you to learn at your own pace without any financial commitment.
4.9
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What you'll learn
Master orthogonal vector operations and dot products
Understand orthogonal projections and transformations
Apply the Gram-Schmidt process
Analyze symmetric matrices and their properties
Solve least-squares problems
Skills you'll gain
This course includes:
2.6 Hours PreRecorded video
11 quizzes
Access on Mobile, Tablet, Desktop
FullTime access
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There are 4 modules in this course
This comprehensive course focuses on advanced linear algebra concepts, particularly orthogonality and diagonalization. Students learn about orthogonal vectors, transformations, and symmetric matrices, with applications to AI and machine learning. The curriculum covers dot products, orthogonal projections, the Gram-Schmidt process, and quadratic forms. Special emphasis is placed on symmetric matrices and their eigenspaces, which are crucial for data science applications.
Orthogonality
Module 1 · 2 Hours to complete
Orthogonal Projections and Least Squares Problems
Module 2 · 3 Hours to complete
Symmetric Matrices and Quadratic Forms
Module 3 · 2 Hours to complete
Final Assessment
Module 4 · 0 Hours to complete
Fee Structure
Individual course purchase is not available - to enroll in this course with a certificate, you need to purchase the complete Professional Certificate Course. For enrollment and detailed fee structure, visit the following: Linear Algebra from Elementary to Advanced
Instructor
Associate Teaching Professor and Director of Online Programs at Johns Hopkins University
Dr. Joseph W. Cutrone is an Associate Teaching Professor and the Director of Online Programs at Johns Hopkins University, where he specializes in mathematics education. He earned his PhD in Mathematics from Johns Hopkins University, with research interests focused on higher-dimensional algebraic geometry. Since 2006, Dr. Cutrone has taught mathematics at various levels, both online and in traditional classroom settings, holding positions at Johns Hopkins, Northwestern University, Towson University, and Goucher College. His commitment to education is reflected in his extensive teaching portfolio, which includes courses such as Algebra, Applied Calculus with Python, and Linear Algebra. Dr. Cutrone is also active in online education, contributing to platforms like Coursera. His scholarly work includes several publications on topics related to algebraic geometry and has been recognized for its impact within the mathematical community.
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