One factor in favor of the use of LLM as a learning tool is the poor quality of documentation. It seems we've forgotten how to write usable explanations that help readers to build a coherent model of the topic at hand.
The idea of tensors as "a matrix of numbers" or the example of a cube with vectors on every face never clicked for me. It was this (NASA paper)[https://www.grc.nasa.gov/www/k-12/Numbers/Math/documents/Ten...] what finally brought me clarity. The main idea, as others already commented, is that a tensor or rank n is a function that can be applied up to n vector, reducing its rank by one for each vector it consumes.
In your cube example you are using the word "vector" to refer to faces of the cube. Did you mean matrix?
My understanding is that the cube is a rank 3 tensor, the faces (or rather slices) of the cube are rank 2 tensors (aka matrices), and the edges (slices) of the matrices are rank 1 tensors (aka vectors).
Math and Physics equations are full of beauty capable of transmit the same joy as poetry. The main difficulty is that they require more study.
For me, looking at Maxwell equations is a source of pleasure. Also, after improving my understanding of the Laplacian, I came to appreciate the heat equation.
The alternative, using general programming languages, is a terrible idea. The last thing I want to do when dealing with a domain specific configuration is trying to figure the meaning out of hundreds of poorly written, badly abstracted, totally undocumented, lines of code.
reply