Linear Algebra with Frames

I have a bunch of notations I like to use for linear algebra and vector calculus which are at this point scattered across various notes and posts. I wanted to consolidate them in one place so that I can refer to them later. I am pretty sure that the ideas in here are useful and that various parts of math and physics would benefit from incorporating them. However, I’m not sure I have figured out the best ways of stating them all yet. Probably I will make some edits to this over time as I settle on better and