A Cross Eigenvalue Condition Matrix
نویسندگان
چکیده
We introduce a cross eigenvalue condition matrix for measuring the sensitivity of eigenvalue computations. A fundamental difference between this new object and traditional eigenvalue condition numbers is that cross interactions between eigenvectors that are not associated with the same eigenvalue are taken into account. We develop an abstract formulation that makes it possible to define continuous and finite quantities for all square matrices, including non-diagonalizable ones. We give applications of our condition matrix to Markov chains, including the PageRank model.
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