Abstract
Using the Clifford algebra techniques of Pryde, Bhatia and Bhattacharyya generalized the classical eigenvalue perturbation bound of Henrici to the joint spectrum of commuting tuples of matrices. Elsner improved on this result. Using the techniques of Pryde and Chu, we show that for small perturbations a smaller bound may be given than that obtained by Elsner. A similar result is then obtained using the technique of Elsner himself.
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