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The paper presents a general theory of coupling of eigenvalues of complexmatrices of arbitrary dimension depending on real parameters. The cases of weakand strong coupling are distinguished and their geometric interpretation in twoand three-dimensional spaces is given. General asymptotic formulae foreigenvalue surfaces near diabolic and exceptional points are presenteddemonstrating crossing and avoided crossing scenarios. Two physical examplesillustrate effectiveness and accuracy of the presented theory.Comment: 19 pages, 8 figure

Coupling of eigenvalues of complex matrices at diabolic and exceptional points