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In linear algebra, the eigengap of a linear operator is the difference between two successive eigenvalues, where eigenvalues are sorted in ascending order.

The Davis-Kahan theorem, named after Chandler Davis and William Kahan, uses the eigengap to show how eigenspaces of an operator change under perturbation.[1] In spectral clustering, the eigengap is often referred to as the spectral gap; although the spectral gap may often be defined in a broader sense than that of the eigengap.

See also


  1. ^ Davis, C.; W. M. Kahan (March 1970). "The rotation of eigenvectors by a perturbation. III". SIAM J. Numerical Analysis. 7 (1): 1-46. doi:10.1137/0707001. 

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