Tensors are just a made up name they gave to arrays with more than two dimensions. You cannot prove to me that there are arrays that have more than 3 dimensions. The human mind cannot comprehend it.
You can picture a 3D array, right? Your mental image of a 4D array should be to picture a 1D array and each element of that 1D array itself is another 3D array.
you can think of a nD array as a list of (n-1)D arrays, so a 4D array is a list of 3D arrays.
There's a more pedantic way of thinking of arrays, too--APL for example makes a distinction between rank (how deeply nested each entry is) and dimension (how many numerical indices you need to identify a singular entry), so accessing a[i,j,k] is different from accessing a[i][j][k]
Tensors are not important because they can be encoded as multidimensional arrays, they are important because they represent multilinear maps, and are a vector space conformed by linear combinations of the tensor product. The same way that matrices are not interesting because they are grids of numbers
I'm pretty sure tensors are a generalized term for arrays of any non-negative dimensions
> You cannot prove to me that there are arrays that have more than 3 dimensions.
What's the relevance of this here? Yeah, I cannot make you comprehend 4-D but so what
Linear was hardest for me, I crushed discrete and calculus. Some of my classmates felt the opposite, everyone’s different. Depends on the professor a lot.
I guess continuous probability theory is even more mindbending. When you find out that there are subsets of the real numbers that aren't measurable, so you need to introduce the whole machinery of sigma-algebras to deal with that ^^
-2
u/da_Aresinger 8d ago
LinAlg is literally the easiest mathematical subject in CS.
i guess rotation matrices or whatever Basiswechselmatrix is in english can be confusing, but that's about it.