These include scalars, spinors, tensors and spinor-tensors. If the scalars have the commutative property, then all four matrices are equal. For example, scalars, arrays, and hashes have different leading sigils. In what follows we will distinguish scalars, vectors and matrices by their typeface. There are a total of nine possibilities using scalars, vectors, and matrices. In array languages, operations are generalized to apply to both scalars and arrays. The subtraction in the numerator is the subtraction of vectors, not scalars. Vectors can be added, subtracted, multiplied and divided by scalars. In 1891 Oliver Heaviside argued for Clarendon to distinguish vectors from scalars. In this article, vectors are represented in boldface to distinguish them from scalars. "Bases" allow one to represent vectors by a sequence of scalars called "coordinates" or "components". Elements of are called "vectors", and elements of "F" are called "scalars". As usual, we call elements of "V" "vectors" and call elements of "K" "scalars". Then the scalars formula 26 completely determine the multilinear function formula 27. When the scalars are real, this map is an isometric isomorphism.