A Bird’s-Eye View of Linear Algebra: Orthonormal Matrices | by Rohit Pandey | Dec, 2024

Orthonormal matrices: the most elegant matrices in all of linear algebra

This is the eighth chapter of the in-progress book on linear algebra: “A birds eye view of linear algebra”. The table of contents so far:

In this chapter, we will cover special kinds of matrices: orthogonal and orthonormal. These kinds of matrices (and the corresponding linear maps they represent) have good properties, from theoretical to numerical that make them easy to work with. For instance, to get the inverse of an orthonormal matrix, you can simply flip it (take its transpose). But we’re getting ahead of ourselves. Let’s understand what it even means for a matrix to be orthonormal.