I'm embarrassed to ask, but I think this will save me some time...(adsbygoogle = window.adsbygoogle || []).push({});

I'm trying to use the condition [itex]\Lambda^T\eta\Lambda=\eta[/itex] to show that [itex]\Lambda_{0i}=-\Lambda_{i0}[/itex], where i=1,2,3. This is the algebraic version of the physically obvious condition that if the velocity associated with a homogeneous Lorentz transformation is [itex]\vec{v}[/itex], then the velocity associated with its inverse is [itex]-\vec{v}[/itex]. This should be easy, but I don't see it.

([itex]X_{0i}[/itex] is row 0, column i, of the matrix X. I'm putting all the indices downstairs because I feel that's less confusing when calculations include transposes of matrices).

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Simple problem driving me nuts :-)

**Physics Forums | Science Articles, Homework Help, Discussion**