Fredholm theory | Linear algebra

Fredholm alternative

In mathematics, the Fredholm alternative, named after Ivar Fredholm, is one of Fredholm's theorems and is a result in Fredholm theory. It may be expressed in several ways, as a theorem of linear algebra, a theorem of integral equations, or as a theorem on Fredholm operators. Part of the result states that a non-zero complex number in the spectrum of a compact operator is an eigenvalue. (Wikipedia).

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Related pages

Vector space | Generalized function | Linear algebra | Elliptic operator | Fredholm operator | Sobolev space | Banach space | Spectral theory of compact operators | Square-integrable function | Fredholm theory | System of linear equations | Mathematics | Spectrum (functional analysis) | Dirac delta function | Weak derivative | Distribution (mathematics) | Convolution | Compact operator | Integral equation | Farkas' lemma | Complex number | Hilbert–Schmidt integral operator | Fredholm integral equation | Fredholm's theorem | Resolvent formalism