Note 1 to entry: General Lorentz transformations form a group. Denoting ${\Omega }_{\text{L}}$ the set of all general Lorentz transformations $L$, following rules are fulfilled:

1. the identity transformation $I$ belongs to ${\Omega }_{\text{L}}$;
2. a composition of general Lorentz transformations is associative, i.e. $L^{\prime }\left(L^{″}{L}^{‴}\right)\text{=}\left(L^{\prime }{L}^{″}\right)L^{‴}$;
3. to any $L$ exists an inverse one $L^{-1}$ such that $L{L}^{-1}=I$.

Note 2 to entry: A general Lorentz transformation is a linear, rotational transformation in space-time.

Note 3 to entry: A general Lorentz transformation for synchronized S, S' can be expressed by $\underset{\_}{\underset{\_}{x^{\prime }}}=L\underset{\_}{\underset{\_}{x}}$ where $L=\left(\begin{array}{cccc}\gamma & -\gamma {\beta }_x& -\gamma {\beta }_y& -\gamma {\beta }_z\\ -\gamma {\beta }_x& 1+\frac{\left(\gamma -1\right){\beta }_x^2}{{\beta }^2}& \frac{\left(\gamma -1\right){\beta }_x^{}{\beta }_y}{{\beta }^2}& \frac{\left(\gamma -1\right){\beta }_x^{}{\beta }_z}{{\beta }^2}\\ -\gamma {\beta }_y& \frac{\left(\gamma -1\right){\beta }_x^{}{\beta }_y}{{\beta }^2}& 1+\frac{\left(\gamma -1\right){\beta }_y^2}{{\beta }^2}& \frac{\left(\gamma -1\right){\beta }_y^{}{\beta }_z}{{\beta }^2}\\ -\gamma {\beta }_z& \frac{\left(\gamma -1\right){\beta }_x^{}{\beta }_z}{{\beta }^2}& \frac{\left(\gamma -1\right){\beta }_y^{}{\beta }_z}{{\beta }^2}& 1+\frac{\left(\gamma -1\right){\beta }_z^2}{{\beta }^2}\end{array}\right)$

In the case where the representation of four-vectors is given by $\underset{\_}{\underset{\_}{x}}=(x_0;\overrightarrow{x})$ and their transposition by ${\underset{\_}{\underset{\_}{x}}}^{\text{T}}:={\left(x_0;\overrightarrow{x}\right)}^{\text{T}}$, then $L=\left(\begin{array}{cc}\gamma & -\gamma {\overrightarrow{\beta }}^{\text{T}}\\ -\gamma \overrightarrow{\beta }& I+\Gamma \end{array}\right)$, where $I$ is the $3\times 3$ identity matrix and ${\displaystyle \Gamma =\frac{\left(\gamma -1\right)}{{\beta }^2}\overrightarrow{\beta }{\overrightarrow{\beta }}^{\text{T}}}$ is a three-dimensional matrix built from the dyadic product of the normalized velocity $\overrightarrow{\beta }$.

Note 4 to entry: The coherent SI unit of the matrix $L$ describing the general Lorentz transformation is one, symbol 1.