Stewart, G. W.This paper describes a method for calculating the condition number of a matrix in the Frobenius norm that can be used to select columns in the course of computing a QR decomposition. When the number of rows of the matrix is much greater than the number of columns, the additional overhead is negligible. Limited numerical experiments suggest that the method is quite good at finding gaps in the singular values of the matrix. Additional files are available via anonymous ftp at: thales.cs.umd.edu in the directory pub/reports (Also cross-referenced as UMIACS-TR-90-87)en-USTechnical Report