Degrees of Freedom

Because our model of evolution is symmetrical, i.e. it does not distinguish a particular sequence, E must be symmetric. It is also easy to see that if we replace E_ij by $\alpha E_{ij} + \beta$ then F(d) does not change (both numerator and denominator are multiplied by $\alpha^2$). Before we do any minimization we have to eliminate these two degrees of freedom. Most of the time this can be done by arbitrarily setting two values of E, e.g. E₁₁ = -1 and E₁₂ = 1.