I am trying to understand the resizing of an image, I understand that it is a matrix and the concept of where the values change when changing its size, but I don't know if this is some operation in linear algebra.
For example, I have a $ [2,2] $ matrix and I want to transform it into $ [6, 6] $ which is to multiply it by $ 6 $, well the rows and columns start with zero (the ones represent pixels)
$$
\begin{matrix}
1 & 1 \\
1 & 1
\end{matrix}
\rightarrow
\begin{matrix}
1 & 0 & 0 & 0 & 1 & 0 \\
0 & 0 & 0 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 & 0 & 0 \\
1 & 0 & 0 & 0 & 1 & 0 \\
0 & 0 & 0 & 0 & 0 & 0 \\
\end{matrix}
$$
another example
$$
\begin{matrix}
1 & 1 & 1 \\
1 & 1 & 1 \\
1 & 1 & 1
\end{matrix}
\rightarrow
\begin{matrix}
1 & 0 & 1 & 0 & 1 & 0 \\
0 & 0 & 0 & 0 & 0 & 0 \\
1 & 0 & 1 & 0 & 1 & 0 \\
0 & 0 & 0 & 0 & 0 & 0 \\
1 & 0 & 1 & 0 & 1 & 0 \\
0 & 0 & 0 & 0 & 0 & 0 \\
\end{matrix}
$$
the first coordinate is $(0,0)$ the second is $(0,1)$ and last $(0,2)$ then double the size then the first coordinate follows while $(0,0)$ the second is $(0, 2)$ and the third is $(0, 4)$
I guess the operation they are doing is the following In the matrix $ A $ for all $ A_{j, i} $ we multiply by a $ \delta $ something like $ i,j * \delta $
After searching I found that it is a resize image algorithm but I still don't know what the mathematical operation is :(
Questions:
So my question is any operation in linear algebra?
Does it have any notation?
sorry English is not my mother tongue