Riemannian Optimization Tutorial? Looking for a good quick guide about Riemannian optimization, from an applied perspective such as machine learning. Referrals to easy to read references would be really appreciated.

I wrote an introductory book for Riemannian optimization, designed for applied mathematicians and engineers:
An introduction to optimization on smooth manifolds
http://www.nicolasboumal.net/book
Chapters 3 and 5 are a stand-alone introduction to Riemannian geometry for the special case of embedded submanifolds of linear spaces. This covers many usual applications of Riemannian optimization, and allows to give precise definitions and full proofs without the need for charts and atlases. Chapters 4 and 6 focus on algorithms. Chapter 7 details some manifolds of interest. Later chapters look at more advanced topics.
