Express the vector
as a matrix for scalars . Show that the determinant of this matrix is 1. Find the inverse matrix. Verify that the inverse matrix is precisely the Inverse Lorentz Transformation (with no boost in the y and z axes).
The Lorentz Transformation:
Since the determinant is 1, we can just find the adjugate matrix. The adjugate matrix can be found by transposing the cofactor matrix. Hence,
We retrieve the Inverse Lorentz Transformation:
Check out my other notes at Proof, Disproof, and Derivation