As I understand a vector is anything with a dimension of n x 1. While a matrix is anything with a dimension of n x n. Where n can be any number.
So, to my knowledge, when we convert a scalar repetitive operation into a single matrix, this is called vectorization. I'll take the example of linear regression, hypothesis function. We convert H(x)=theta0+theta1x into two matrices, X, with a dimension of m x 2, and Theta with a dimension of 2 x 1, where m is the number of training examples. Here one vector is formed, while the other is a matrix. So wouldn't a better term be "matrixiation".
Why have we named it vectorization?