I am interested in the extent of knowledge of Linear Algebra required for Spivak's Calculus on Manifolds. More precisely, in the first problems in his book they reference norm preservation and inner-product preservation with regard to linear transformations and matrices.
I had done Lang's Intro to Linear Algebra but I don't feel like I learned enough to be able to handle the assumed knowledge in Spivak's book. I could work through Lang's Linear Algebra if I need to in order to gain the necessary background since I seem to have not gained it from the introductory book.
Does this seem like it would be a good book to prepare me? Perhaps others would be more suitable? I also had Strang's Linear Algebra and It's Applications