For simplicity, look at the infinitesimal Lorentz boost in the x direction (examining a boost in any other direction, or rotation about any axis, follows an identical procedure). The infinitesimal boost is a small boost away from the identity, obtained by the Taylor expansion of the boost matrix to first order about ζ = 0, B x = I + ζ ζ ∂ ∂ B x ∂ ∂ ζ ζ | ζ ζ = 0 + ⋯ ⋯ where the higher order terms not shown are negligible because ζ is small, and B x is simply the boost matrix in the x direction. The derivative of the matrix is the matrix of derivatives (of the entries, with respect to the same variable), and it is understood the derivatives are found first then evaluated at ζ = 0, ∂ ∂ B x ∂ ∂ ζ ζ | ζ ζ = 0 = − − K x .