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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.
by mvaliente2001 2y ago
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/Tensors_TM2002211716.pd 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.
- cryptonector 2y ago> a tensor or rank n is a function that can be applied up to n vector There seems to be a grammar problem here.
- qsdf38100 2y agoIn 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).
- Koshkin 2y agoBut, in practice, how often do we ask a tensor to consume a vector?