What Is a Vector? It depends! Geometric perspective vs Linear Algebra vs ℝⁿ

[ChaineYTXF]

Professor, did you study in France or in a French speaking country? Or have some French colleagues? Because "sens" and "direction" is a distinction I never hear in English courses! Only in France!
Superb channel. Long time fan here

[freddupont]

You are mentioning homework and exercises in the intro of the lesson; is there a link to them?

[SkeletalBasis]

Quick request: maybe you could do a side video reconciling the notion that geometric vectors all proceed from one arbitrarily chosen point (on the one hand) with the tip-to-tail rule (on the other), which requires that they be all over the place? It looks to me that this would require a not entirely trivial construction involving equivalence classes of lines or rays, plus whatever else it takes to define 'sense' in the directional sense. One point of interest is that this would illustrate what it takes to advance from intuition to consistency --- a central issue in almost all kinds of thought.

[ReginaldCarey]

You can’t introduce dU without complex numbers. Similarly you can’t claim scalar vector multiplication scales the magnitude but then glibly introduce scaling by a negative number as reversing the direction.

If a vector is a magnitude and direction, dU must represent a change in magnitude and a change in direction.

-1 is a really bad representation of i^2.

[juliavixen]

Unrelated to the content of this video, you need to turn off the auto focus of your video camera. Neither the camera nor the whiteboard are moving, so set the focus once at the beginning (verify it's in focus), and lock it so the camera will not change the focus of the lens.

[ReginaldCarey]

The full math is revealed when you stop restricting yourself to real scalars.