Vector · Matrix · Tensor
Same idea, one more axis each time. A vector is a row. A matrix is a waffle. A tensor is a syrup-drenched stack of waffles on a plate.
Vector
1 axis · lengthA single row of numbers along one axis. A token embedding is a vector — e.g. 12,288 slots, each a single scalar coordinate.
Matrix
2 axes · rows × columnsA grid of numbers with two axes. Stack many vectors and each vector becomes one row. The embedding matrix is exactly this: every token in the vocabulary is a row.
Tensor
3+ axes · rows × columns × depthA stack of matrices — a third axis on top of rows × columns. Picture a stack of waffles on a plate: one waffle is a matrix (its pockets are the numbers), and piling waffle on waffle adds depth. The syrup poured over the whole stack is the operation that links them — in a transformer, that's attention flowing across every layer at once, mixing the numbers between waffles. That stacked, syrup-linked shape is exactly what the model computes on.