I'm slightly confused on how the inner product scales here - isn't the project of v onto 2u still the same?
Does the projection idea only hold for unit vectors? I'm confused because it doesn't seem to hold for all the examples behind? What is an actual use case if that's true?
It makes sense why the projection of 2v onto u would be twice the projection of v onto u, but what if you're projecting v onto 2u instead? Why is that still twice the projection of v onto u? The symmetry seems unintuitive here.
Sometimes I've heard the word "projection" used to describe the vector of the projection of, in this case, v onto u. In this class, when you ask for or describe a projection value, are you describing just the magnitude of the "shadow" of v onto u?
Based on the diagram, I'm confused as to why projecting v onto u would double (while the math seems t0 make sense), as the diagram never shows that projecting v would change.
This doesn't make sense to me - to generalize what the others are saying, it seems like by this visual explanation, the projection is only dependent on the magnitude of the vector being projected (and not the magnitude of the vector being projected onto. However, by the mathematical definition of an inner product, it should be dependent on both.