Aiming at the defect of traditional spectral dimension reduction method, a new method based on the matrix theory is presented. The matrix is the revision of the matrix R theory defined by Cohen. Object spectral reflectance can be decomposed into the fundamental spectrum and the metameric black spectrum, and then linear dimension reduction is carried respectively. Three basis functions of the fundamental spectrum whose percent variance reach 100% are the orthogonal result of the color-matching functions multiplied with illuminant. The basis functions of the metameric black are derived by principal component analysis. Results of experiment show that the proposed model improves spectral and colorimetric accuracy of reconstructed spectra and satisfies the requirement of spectral color reproduction.