A matrix lower bound |
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Authors: | Joseph F Grcar |
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Institution: | 6059 Castlebrook Drive, Castro Valley, CA 94552, USA |
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Abstract: | 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 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. |
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Keywords: | 15A45 15A03 15A60 65F35 90C47 |
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