The linear summability of inherent optical properties (IOPs) is exploited to provide matrix equations for retrieval of phytoplankton absorption, dissolved organic matter, and constituent backscatter. Spectral models for the phytoplankton pigment absorption coefficient, chromophoric dissolved organic matter (CDOM) absorption coefficient, and total constituent backscatter (TCB) coefficient are first used to calculate 5¿105 water-leaving spectral radiances for a wide range of normally distributed IOP values at 410, 490, and 555 nm. Then, the spectral radiances are inverted to simultaneously provide phytoplankton pigment absorption coefficient, CDOM absorption coefficient, and total constituent backscatter coefficient on a pixel-by-pixel basis to demonstrate that (1) matrix inversion is very rapid and well conditioned, (2) the IOPs are exactly determined when the water-leaving radiances and IOP spectral models are error free, (3) for equal radiance errors sequentially occurring in one of three sensor bands, phytoplankton pigment retrieval errors are generally higher than CDOM and TCB coefficient errors, (4) retrieval errors for all the IOPs are strongly dependent on phytoplankton pigment spectral model Gaussian width errors, (5) phytoplankton pigment absorption and CDOM absorption retrieval errors are more sensitive to CDOM spectral slope errors than the TCB coefficient retrievals, and (6) TCB wavelength-ratio-exponent errors produce less impact on the phytoplankton absorption coefficient retrieval than upon the CDOM absorption or the TCB coefficient retrievals. ¿ American Geophysical Union 1996