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Derivatives of the spectral radius as a function of non-negative matrix elements

Published online by Cambridge University Press:  24 October 2008

Joel E. Cohen
Joel E. Cohen
Affiliation:
The Rockefeller University, New York
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Extract

Let A = (aij) be a non-negative n × n matrix, that is, aij ≥ 0, i, j = 1, …, n; n > 1. We write A ≥ 0. Let r = r(A) be the spectral radius of A; assume r > 0 throughout to avoid trivial cases. Let be the mth derivative of r with respect to the element aij, all other elements of A being held constant.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 83 , Issue 2 , March 1978 , pp. 183 - 190
Copyright
Copyright © Cambridge Philosophical Society 1978

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References

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