The underlying idea appeals to me.In the next few days, I will read your proposal in more detail to give you a complete feedback, but for the moment I will focus on the basic design.
I think you are bitting off more than you can chew, among new classes, new functions, and new concepts. Your implementation would be great for a custom library that provides containers for linear algebra operations, but it is too restrictive and full-bodied for an update to the C++ standard.
I do not agree with introducing new classes that involve direct memory management, in particular if there are two versions that provide static memory and dynamic memory separately, because I believe they are redundant with the already-existing STL containers, such as std::vector and std::array (it is effectively used in your implementation of fixed size classes).
I think you may avoid this by creating adapters, like std::flat_set / std::flat_map, that provides different interfaces to perform linear algebra operations and do not worry about anything at lower level.