Inner product spaces, quadratic forms, and more advanced problem solving ,What you’ll learn:
How to solve problems in linear algebra and geometry (illustrated with 144 solved problems) and why these methods work.
Solve more advanced problems on eigendecomposition and orthogonality than in the second course.
The third course in Linear Algebra and Geometry explains the inner product in Euclidean spaces, quadratic forms, and minimization problems. You will also learn how to solve more advanced problems on eigendecomposition, orthogonality, etc. The course contains a large numbers of examples and problem sets that are thoughtfully designed to help you practice these methods.
This course on linear algebra and geometry is the next step in my series of highly abstract, theoretical courses on mathematics. The first two courses in this series are “Linear Algebra 1” and “Linear Algebra 2”. This course continues with more advanced topics and problem solving than in those two previous courses. We start by defining inner products, with a focus on how they can be used to solve geometric problems. We then go onto quadratic forms and their eigendecomposition. Then back to geometry with theorems of Grassmann and Cauchy-Schwarz, before ending with questions about transformations induced by orthogonal matrices.
