In mathematics, the spectral gap is the difference between the
moduli of the two largest
eigenvalue
In linear algebra, an eigenvector () or characteristic vector of a linear transformation is a nonzero vector that changes at most by a scalar factor when that linear transformation is applied to it. The corresponding eigenvalue, often denoted b ...
s of a matrix or operator; alternately, it is sometimes taken as the smallest non-zero eigenvalue. Various theorems relate this difference to other properties of the system.
See also
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Cheeger constant (graph theory)
In mathematics, the Cheeger constant (also Cheeger number or isoperimetric number) of a graph is a numerical measure of whether or not a graph has a "bottleneck". The Cheeger constant as a measure of "bottleneckedness" is of great interest in ma ...
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Cheeger constant (Riemannian geometry)
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Eigengap 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 ei ...
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Spectral gap (physics)
In quantum mechanics, the spectral gap of a system is the energy difference between its ground state and its first excited state. The mass gap is the spectral gap between the vacuum and the lightest particle. A Hamiltonian with a spectral gap is ...
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Spectral radius
In mathematics, the spectral radius of a square matrix is the maximum of the absolute values of its eigenvalues. More generally, the spectral radius of a bounded linear operator is the supremum of the absolute values of the elements of its spectru ...
References
External links
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{{Mathanalysis-stub
Spectral theory