In the context of Machine Learning, it is convenient to think of a tensor as an $n$-dimensional array. Tensor dimensionality is also commonly referred to as its order, degree or rank, which formally is the sum of the tensor contravariant and covariant indices.

The dot product is an algebraic operation which takes two equal-sized vectors and returns a single scalar (which is why it is sometimes referred to as the scalar product). In Euclidean geometry, the dot product between the Cartesian components of two vectors is often referred to as the inner product.