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This question probably is extremely trivial and silly, but I haven't been able to find the answer to it despite going through quite a bit of The Internet.

So, it appears that each Quantum Logic Gate corresponds to a matrix. Ones that interact with one qubit are 2 x 2, two qubits 4 x 4. The problem is, I have no clue what on Earth these matrices do and how they correspond to the gates. Do you multiply them by something? If so, what is that something?