Situations are analyzed where repetitive measurements are performed on similar physical situations. One measurement is assumed to produce one column vector of numbers. Together, the measurements produce a matrix Aij. By "similar" we mean that the columns of matrix A can be represented as linear combinations of some possible unknown basis vectors plus noise. It is shown how the singular value decomposition (SVD) of matrix A is used to analyze the contents of the matrix: the amount of noise-like experimental error is revealed, and more importantly, the presence or non-presence of any kind of distortions from the ideal situation is quantitatively estimated. The result of this analysis is summarized as the "quality number" Q of a matrix. A low Q is a warning: there is something wrong in your data. A high Q is a positive indication of the quality of the data. Experimental examples from X-ray physics are studied. It is demonstrated how SVD aids in a correction process, whereby the distortions are removed from matrix A. © 1990.
