Real norms are not complex

L. Ridgway Scott. 2 November, 2012.
Communicated by L. Ridgway Scott.


We provide alternate derivations of some results in numerical linear algebra based on a representation of the action of a real matrix on real vectors in the case that it has complex conjugate eigenvalues. We consider two applications of this representation. The first one is to the relationship between the spectral radius and the norm of a matrix. The second relates the spectral radius and the limits of norms of roots of powers of a matrix.

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