针对传统光谱降维方法的缺点，提出一种基于矩阵理论的线性光谱降维方法。该方法在Cohen定义的矩阵R理论基础上提出修正矩阵，可将物体光谱反射率分解为基本光谱和同色异谱黑光谱，再分别对两者进行线性降维。基本光谱的三个基向量由颜色匹配函数与光源的乘积再进行正交化得到，其三个基向量的累积贡献率可达100%。同色异谱黑光谱的基向量由主成分分析推导，取前三个特征向量作为同色异谱黑光谱的基向量。实验结果表明，使用该方法构建的六维线性模型能在光谱和色度两个方面较好地表征原始高维光谱反射率，满足光谱颜色复制的要求。

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.