A matrix lower bound [report]

Joseph F. Grcar
2002 unpublished
Submitted by R.A. Brualdi AMS classification: 15A45 15A03 15A60 65F35 90C47 Keywords: Matrix inequalities Distance to lower rank Functional analysis in matrix theory Condition number Four essentially different interpretations of a lower bound for linear operators are shown to be equivalent for matrices (involving inequalities, convex sets, minimax problems, and quotient spaces). Properties stated by von Neumann in a restricted case are satisfied by the lower bound. Applications are made to rank
more » ... reduction, s-numbers, condition numbers, and pseudospectra. In particular, the matrix lower bound is the distance to the nearest matrix with strictly contained row or column spaces, and it occurs in a condition number formula for any consistent system of linear equations, including those that are underdetermined.
doi:10.2172/836372 fatcat:k2p3uqq7pjegbdi3go6w36o7oa