Derivatives of the spectral radius as a function of non-negative matrix elements
- 1 January 1978
- journal article
- research article
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 83 (2) , 183-190
- https://doi.org/10.1017/s0305004100054438
Abstract
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.Keywords
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