I was studying special relativity and i found this derivation of the Lorentz transformations \begin{equation} \left( \begin{array}{cccc} x'^0 \\ x'^1 \\ x'^2\\ x'^3 \end{array} \right)= \left( \begin{array}{cccc} \gamma & -\gamma \beta & 0& 0 \\ -\gamma \beta &\gamma &0 & 0 \\ 0 & 0 & 1 & 0\\ 0 & 0 & 0 & 1 \end{array} \right)\left( \begin{array}{cccc} x^0 \\ x^1 \\ x^2\\ x^3 \end{array} \right) \end{equation}
and then he denotes \begin{equation} Λ^μ{}_ν= \left( \begin{array}{cccc} \gamma & -\gamma \beta & 0& 0 \\ -\gamma \beta &\gamma &0 & 0 \\ 0 & 0 & 1 & 0\\ 0 & 0 & 0 & 1 \end{array} \right) \end{equation} as the lorentz transformation matrix. If that's the case which matrix is for example $Λ_{νμ}$ or $Λ^{νμ}$ or even $Λ_μ^ν$.I am confused about which matrix is which.
Anyone to clarify?
Also, how do i know which index is first meaning is it $Λ_{ν}{}^{\ μ}$ or $Λ^μ{}_{\ ν}$?
I will appreciate if you have any reference to check these.