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
Linear Algebra: Orthogonality and Diagonalization
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11 项作业
授课语言：英语（English）
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本课程是 Linear Algebra from Elementary to Advanced 专项课程 专项课程的一部分
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该课程共有4个模块
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.
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2个视频2篇阅读材料3个作业
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.
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3个视频3篇阅读材料4个作业
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.
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MD
5
已于 Nov 4, 2024审阅
It is great, the guy on the videos knows a lot, its a pity he writes so fast :))
HK
5
已于 Dec 8, 2024审阅
Teach good. It explore some of my blind areas about diagonalization, eigen and orthogonal, repeated roots concern, etc.
CC
5
已于 Mar 30, 2025审阅
Well taught, clearly explained, thorough and helpful examples throughout
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To access the course materials, assignments and to earn a Certificate, you will need to purchase the Certificate experience when you enroll in a course. 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.
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