Uploaded March 2019 | Updated September 2026, 2 weeks ago

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In this video, I describe the meaning of contravariant and covariant vector components. As mentioned in a previous video, tensors are invariant under coordinate transformations. However, tensor components transform according to specific rules; they may either transform in a contravariant manner (i.e. the opposite manner as the basis vectors) or in a covariant manner (i.e. the same manner as the basis vectors).

I discuss contravariant and covariant components and give some intuition of what they mean by using two examples. The next video will cover a more rigorous definition of contravariant and covariant vector components.

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Pre-reqs: The previous videos in the playlist - youtube.com/playlist?list=PLdgVBOaXkb9D6zw47gsrtE5XqLeRPh27_
2nd video on Tensors: youtube.com/watch?v=j6DazQDbEhQ&list=PLdgVBOaXkb9D6zw47gsrtE5XqLeRPh27_&index=3&t=0s
Lecture Notes: drive.google.com/open?id=1CVYgE5iEGAeuSe16L1x0ULYiL0GVTgJn
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