Extracting Experimental Information from Large Matrixes. 1. A New Algorithm for the Application of Matrix Rank Analysis

Abstract

For many, especially complex, systems, modern spectroscopic measurements can be generated as large experimental data sets in matrix form. We report a new algorithm for the application of matrix rank analysis to extract significant experimental information from these large matrixes. The algorithm may be used to detect and remove erroneous rows and/or columns from the matrixes and to monitor the most significant experimental information along the rows and/or columns of the data sets. A new method for determining the number of absorbing species and a new concept for the treatment of experimental errors are presented. The algorithm is illustrated on real experimental examples.