Based on the weak intensity/phase modulation transfer matrix H, a matrix V for intensity noise (IN) and phase noise (PN) evolution along nonlinear, dispersive and lossy fiber is derived, while matrix description makes it especially useful in noise evolution analysis in systems with chained optical amplifiers. Evolution of two noise sources, laser phase noise and ASE of EDFA, is examined in detail through V. IN, PN and optical field noise spectral densities are studied uniformly. Correspondingly, electrical signal-to-noise ratio (SNRe), equivalent linewidth ((Delta) (upsilon) eq and optical signal-to-noise ratio (SNRo) are used to characterize system performance. It is found that for IM systems, an optimal P0 corresponding to minimum SNRe exists in positive dispersion fibers, and input optical power cannot be arbitrarily increased to improve SNRe even though only noise is considered. On the contrary, in negative dispersion fibers, SNRe is improved with increasing P0 monotonously. For PM systems with negligible laser phase noise and regardless of the sign of fiber dispersion, an optimal optical power also exists to ensure minimum phase noise. SNRo, a combined contribution from intensity and phase noise, is better in fibers with negative dispersion than that in fibers with positive dispersion under the same P0.