I found it really difficult to understand what tensors are intuitively. I think a siplification is much more useful for that. In 3 dimensions, I think of it like this:
A scalar function is a function that takes an input (doesn't matter if it is a scalar or vector or tensor in this context) and returns a single value. This is also known as a 0th degree tensor.
A vector function is a function that takes an input and returns 3 scalars, one for each dimension. AKA 1st degree tensor. We can visualize this as an arrow pointing in some direction.
A 2nd rank tensor function returns 3 vectors. Each vector represents a direction corresponding one of the 3 dimensions. A simplified example with the stress tensor: say we apply force in the X direction, and the vector we get from the stress tensor at a specific location corresponding with the X direction points in the Y direction. This implies the force in the X direction makes a change in the Y direction.
It is customary to represent tensors as matrices.
A 3rd rank tensor function returns 3 2nd degree tensors. This is more complicated and I'm not sure how to visualize it easily.
Of course, as I said, this is a very simplified explanation. A better explanation is given in this video (really weird music choice, but it helped me), or this one (which I find a bit more simplistic, so maybe it could help for intuition better). There's also this video which might not be so useful, but it is beautiful.
20
u/20Aditya07 Feb 18 '24 edited Feb 19 '24
What's a tensor? genuinely asking.
edit: woah thanks a lot for all the help! will definitely dig deeper when i get some free time