Two observers A and B, in different initial system describe the same physical event with their particular, different space time coordinates . Let the coordinate of the event be $x^\mu$ for observer A and ${x^\prime}^\mu$ for observer B .Both coordinates are connected by means of the Lorentz transformation. $${x^\prime}^\mu = \sum_{\mu=0}^{3}a^{\nu}_{\mu}x^\mu\equiv a^{\nu}_{\mu}x^\mu\ = (\hat{a}\overset{\Rightarrow}{x})$$ Where $\hat{a}$ denotes the abbreviated version of the transformation matrix and $\overset{\Rightarrow}{x}$ is a 4 dimensional world vector .
I need to understand the Lorentz transformation equation that how it transformed .
EDITED : How both coordinates are connected in that transformation .
