Johns Hopkins University via Coursera
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.
The theory, skills and techniques learned in this course have applications to AI and machine learning. In these popular fields, often the driving engine behind the systems that are interpreting, training, and using external data is exactly the matrix analysis arising from the content in this course.
Successful completion of this specialization will prepare students to take advanced courses in data science, AI, and mathematics.
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 o…
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 ar…
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 specia…
Some points apply to every course of this kind; see how we rank.
Johns Hopkins University is in Tier 1: world-leading universities and India's top institutes of our institution ranking (93/100).
Instructor(s): Tom Leighton, Marten van Dijk This course covers elementary discrete mathematics. Mathematical definitions and proofs are emphasized. Topics include formal logic, induction, graph theory, asymptotic notation and growth of functions, counting principles, and discrete probability.
Harvard University · edX
Contracts are a part of our everyday life, arising in collaboration, trust, promise and credit. How are contracts formed? What makes a contract enforceable? What happens when one party breaks a promise?
Our economic institutions, organizations, and skills have not kept up with rapid advances in AI. In this growing gap lie many of society’s greatest challenges and opportunities. This course will explore how AI can and will transform our economy and society in the coming years. Each week, we will le…
Harvard University · edX
This introduction to moral and political philosophy is one of the most popular courses taught at Harvard College.
Harvard University · edX
Learn about successful collaborations between families and educators and why they lead to improved outcomes for students and schools.
Harvard University · edX
Learn how to protect children from violence, exploitation, and neglect through law, policy, and practice in a human rights framework.
