When is a matrix a contraction?
Let A be a nxn matrix with real entries. I think it is well-known that
A^n x -> 0 for all x in R^n iff all eigenvalues of A have absolute values less
than 1.
My question is: In this case, does there exist a norm on R^n such that A is
a contraction relative to the metric defined by the norm?
Where can I find a proof?
.
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