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Lorentz-Invariant Second-Order Tensors and an Irreducible Set of Matrices
We prove that, up to multiplication by a scalar, the Minkowski metric tensor is the only second-order tensor that is Lorentz-invariant. To prove this, we show that a specific set of three $4\times 4$ matrices, made of two rotation matrices plus a Lorentz boost, is irreducible.
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