What is the relation between orthogonal arrays and orthogonal matrices? In software testing, there is this concept of orthogonal arrays. It is said that these arrays are actually matrices but when I google "orthogonal matrix", it says it is a square matrix. These orthogonal arrays are certainly not square, e.g. this one:
111
122
212
221

Is there a  relation between orthogonal arrays and orthogonal matrices, and if so, what is it?

I don't know what you mean by "Orthogonal Arrays", but in the mathematical context, an orthogonal matrix is a matrix $A$ that satisfies $AA^T=A^TA=I$
For this to hold, $A$ has to be a square matrix, otherwise the dimension of $AA^T$ and $A^TA$ will be different and they won't be equal.
And they are called orthogonal matrices because the columns of these matrices are orthogonal, meaning if $A$ is orthogonal, and $v,u$ are column vectors of $A$, then the inner product $<v,u>=0$ if $v\neq u$
