I'm new to the topics of quantum computing in the theory of computation. However, I'm quite lost trying to understanding the mechanism of how to XOR 2 simple matrices.
$A \oplus B$ given $A = \begin{bmatrix} 0 \\ 1 \\ \end{bmatrix}$ and $B = \begin{bmatrix} 1 \\ 0 \\ \end{bmatrix}$
to get the result of $A \oplus B$ = $\begin{bmatrix} 0 \\ 1 \\ 0 \\ 0 \\ \end{bmatrix}$ Although I am attempting on figuring out myself, I am quite running out of time. Therefore, I really look for the responsive explanation from you guys. I have tried looking up those things online, but I haven't got any relevant sources worth explaining its fundamental.
Thanks,
That's not an XOR, it's a tensor product, also called the Kronecker Product. Think of copying the second vector, and multiplying it against the first vector:
$A \otimes B = \begin{bmatrix} 0 \cdot B \\ 1 \cdot B\\ \end{bmatrix} = \begin{bmatrix} 0 \\ 0\\ 1 \\ 0 \end{bmatrix}$