Learn how orthogonality supports matrix methods and how linear transformations describe relationships between vector spaces. Drawing on content from Jeffrey Holt, author of Linear Algebra with Applications, published by Macmillan Learning, this course connects advanced linear algebra techniques with practical problem solving.

You will begin with dot products and orthogonal sets, then use projections and the Gram–Schmidt process to construct orthogonal vectors. You will study diagonalization of symmetric matrices, QR factorization, and singular value decomposition, and apply orthogonality-based methods to least squares regression. You will then examine the definition and properties of linear transformations. You will identify isomorphisms, represent transformations with matrices, and use similarity to understand relationships between matrix representations. Through readings and homework, you will practice these techniques and strengthen your ability to work with transformations between vector spaces. 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.