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All spectral dominant norms are stable

1984; Elsevier BV; Volume: 58; Linguagem: Inglês

10.1016/0024-3795(84)90206-4

1873-1856

Shmuel Friedland, Christoph Zenger,

Matrix Theory and Algorithms

A vector norm |·|on the space of n×n complex valued matrices is called stable if for some constant K&>0, not depending upon A or m, we have |Am|⩽K|A|m We show that such a norm is stable if and only if it dominates the spectralradius.