Orthonormal matrices: probably the most elegant matrices in all of linear algebra
That is the eighth chapter of the in-progress ebook on linear algebra: “A birds eye view of linear algebra”. The desk of contents to this point:
On this chapter, we are going to cowl particular sorts of matrices: orthogonal and orthonormal. These sorts of matrices (and the corresponding linear maps they symbolize) have good properties, from theoretical to numerical that make them straightforward to work with. As an example, to get the inverse of an orthonormal matrix, you possibly can merely flip it (take its transpose). However we’re getting forward of ourselves. Let’s perceive what it even means for a matrix to be orthonormal.