Learn how inner products extend familiar vector concepts and support applications in advanced linear algebra. Drawing on content from Jeffrey Holt, author of Linear Algebra with Applications, published by Macmillan Learning, this course connects inner product spaces with quadratic forms, optimization, and complex vector spaces.

You will begin by calculating and using inner products, then apply the Gram–Schmidt process in inner product spaces. Through examples and practice problems, you will examine applications of these concepts. You will then analyze quadratic forms and positive definite matrices and solve constrained optimization problems. The course also introduces complex vector spaces and Hermitian matrices, extending your study beyond real vector spaces. Readings, practice exercises, and homework give you opportunities to apply these methods across related problems. The course assumes familiarity with systems of linear equations, Euclidean vectors, matrices, subspaces, and determinants. This course is part of the Advanced Topics in Linear Algebra and Applications Specialization and can also be taken independently.