One exponent, say [ x 1 ] , may be chosen arbitrarily, for example [ x 1 ] = − − 1 . In the language of dimensional analysis this means that the exponents N count wave vector factors (a reciprocal length k = 1 / L 1 ). Each monomial of the Lagrangian thus leads to a homogeneous linear equation ∑ ∑ E i , j N j = 0 for the exponents N . If there are M (inequivalent) coordinates and fields in the Lagrangian, then M such equations constitute a square matrix. If this matrix were invertible then there only would be the trivial solution N = 0 .