Scaling and structural condition numbers
Structurally singular matrices are those whose zero patterns determine whether or not they are singular. For other matrices, the structural condition number is the ratio of the maximum absolute value of an entry to the supremum of \(\delta\) such that if we replace any entry smaller than that with zero, we get a structurally nonsingular matrix. The author characterizes the structural condition number in terms of submatrices, gets an upper bound on the structural condition number of doubly stochastic matrices, and obtains a condition for optimal scaling of symmetric matrices.
scientific article; zbMATH DE number 1067948