Topical Bias in Generalist Mathematics Journals

Generalist mathematics journals exhibit bias toward the branches of mathematics by publishing articles about some subjects in quantities far disproportionate to the production of papers in those areas within all of mathematics.Comment: 8 pages, 3 figure

Spectral Condition Numbers of Orthogonal Projections and Full Rank Linear Least Squares Residuals

A simple formula is proved to be a tight estimate for the condition number of the full rank linear least squares residual with respect to the matrix of least squares coefficients and scaled 2-norms. The tight estimate reveals that the condition number depends on three quantities, two of which can cause ill-conditioning. The numerical linear algebra literature presents several estimates of various instances of these condition numbers. All the prior values exceed the formula introduced here, sometimes by large factors.Comment: 15 pages, 1 figure, 2 table