Geodesics and connexions on matrix Lie groups (2015 ed.)

These notes present some elementary considerations on Geodesics and Connexions on Matrix Lie Groups. As motivating examples two sections with special attention to the mechanics of solid bodies are included. This text is originally intended as and grew out of an Appendix to my Lecture Notes on 'Tensor Calculus and Differential Geometry'. The only prerequisites are some skill in 'Calculus in IRn' and 'Elementary Linear Algebra'. The text mainly concerns 'Advanced Matrix Theory'. It could be useful for numerical calculations. In this new (2015)-edition the proofs in Ch. 5-7 have been somewhat extended. Also some alternative viewpoints have been added there.