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Given: g[itex]_{ρσ}[/itex] = g[itex]_{μ\nu}[/itex][itex]\Lambda[/itex][itex]^{μ}[/itex][itex]_{ρ}[/itex][itex]\Lambda[/itex][itex]^{\nu}[/itex][itex]_{σ}[/itex] equation (1)

It was then mentioned to take the 00 entry of equation (1):

So, it went like 1= [itex]\Lambda[/itex][itex]^{ρ}[/itex][itex]_{0}[/itex]g[itex]_{ρσ}[/itex][itex]\Lambda[/itex][itex]^{σ}[/itex][itex]_{0}[/itex] equation (2)

then equation (2) was set equal to ([itex]\Lambda[/itex][itex]^{0}[/itex][itex]_{0}[/itex])[itex]^{2}[/itex] - ([itex]\Lambda[/itex][itex]^{i}[/itex][itex]_{0}[/itex])[itex]^{2}[/itex] equation (3)

I didn't understand how did equation (3) show up, I thought it might be related to s[itex]^{2}[/itex] = x[itex]^{0}[/itex][itex]^{0}[/itex] - x[itex]^{i}[/itex]x[itex]^{i}[/itex] but then what does the vector x[itex]^{μ}[/itex] have to do with [itex]\Lambda[/itex][itex]^{μ}[/itex][itex]_{μ}[/itex].

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# Taking the zero entry of the following

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