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I'm embarrassed to ask, but I think this will save me some time...

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).

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).

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