Brian Ripley always said that everything in R is a vector. The rule also explains tensors.
Ask R for length(3) and it answers 1. A matrix is a vector too, with a dim attribute that says how to fold it. Set dim(x) <- c(2, 3, 4) on 24 numbers and you have a three-way array, its numbers in their original order.
I think he may have said simply that everything is a vector. That holds outside R too: NumPy stores a tensor as one flat run of numbers, plus the shape and step sizes for reading it. A NumPy transpose changes the reading, not the numbers.
I’ve been putting together a workshop, Tensors for Machine Learning, for Universidad El Bosque in Bogotá on 2 October. It starts from the same place: one number, then a vector, a matrix, a tensor.
Numbers. Sit. In. Line. Shapes. Fold. Them. Into. Tensors.
References
- Kalia, R. (2026). The Professor Who Let Us Break R First.
- Kalia, R. (2026). Tensors for Machine Learning. Workshop, Universidad El Bosque, Bogotá.