notes / Studies in Algebra and Group Theory / chapter 4: Categories, Bilinear Forms and Inner Products / From my notebooks

N24 Orthogonal Operators

In progress: these notes stop partway.

(Notebook topic: Lec 16.)

Let be an inner product. We want maps that preserve lengths and angles.

Definition N24.1 (Orthogonal operator). is an orthogonal operator if for all , preserves lengths and angles is an isometry.

(A separate line at the top of the right-hand column, not connected to the above: assume there exists some set of bijective functors.)