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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.