Cones, Graphs and Optimal Scalings of Matricest

نویسندگان

  • B. DAVID SAUNDERS
  • HANS SCHNEIDER
چکیده

Characterizations are given of the optimal scaiings of a complex square matrix within its diagonal similarity class and its restricted diagonal equivalence class with respect to the maximum element norm. The characterizations are in terms of a finite number of products, principally circuit and diagonal products. The proofs proceed by reducing the optimal scaling problems from the multiplicative matrix level in succession to an additive matrix level, a graph theoretic level, and a geometric level involving duality theorems for cones. At the geometric level, the diagonal similarity and the restricted diagonal equivalence problems are unified.

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تاریخ انتشار 1979