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Prove that the proper orthochronous Lorentz group is a linear group
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[QUOTE="TaliskerBA, post: 4320651, member: 261470"] Sorry that'd be ab[itex]_{44}[/itex] = a[itex]_{41}[/itex]b[itex]_{14}[/itex] + a[itex]_{42}[/itex]b[itex]_{24}[/itex] + a[itex]_{43}[/itex]b[itex]_{34}[/itex] + a[itex]_{44}[/itex]b[itex]_{44}[/itex]. So could you set [itex] u [/itex]= (a[itex]_{41}[/itex]/a[itex]_{44}[/itex],a[itex]_{42}[/itex]/a[itex]_{44}[/itex], a[itex]_{43}[/itex]/a[itex]_{44}[/itex])[itex]^{T}[/itex] and [itex] v [/itex]= (b[itex]_{14}[/itex]/b[itex]_{44}[/itex],b[itex]_{24}[/itex]/b[itex]_{44}[/itex], b[itex]_{34}[/itex]/b[itex]_{44}[/itex])[itex]^{T}[/itex]? I'm assuming we want to show the dot product is positive, but not sure of an easy way to figure it out (I'm trying to spot something more than anything). Is there are easy way to show that the direction of these vectors are within 90 degrees of each other? [/QUOTE]
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Prove that the proper orthochronous Lorentz group is a linear group
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