This paper compares the Lyapunov exponents spectrum computation utilizing group theoretical representations of orthogonal matrices applied to decompositions of the tangent map with the Gram-Schmidt Reorthonormalization method. Former method formulates an initial value problem for a system of differential equations and numerically solves them to obtain the Lyapunov exponents. A consequence of this method is the separation between the exponents and the angles pieces in the evolution equations. To illustrate the application of these methods to 2-dim and 3-dim systems, we turn to the standard test case of driven dissipative oscillator in periodic potential and the Lorenz equations. Some experimental observations are given for these systems.