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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?

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    $\begingroup$ Matrices can have dimension $n \times p$ -- that is, matrices don't have to be square. $\endgroup$
    – Sycorax ♦
    May 10, 2020 at 23:28
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    $\begingroup$ All matrices are a fortiori vectors. The term "vectorization," though, comes from computer science, not stats or mathematics. $\endgroup$
    – whuber ♦
    May 11, 2020 at 12:17

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