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.
Other articles related to "fredholm alternative, fredholm":
... In more precise terms, the Fredholm alternative only applies when K is a compact operator ... From Fredholm theory, smooth integral kernels are compact operators ... The Fredholm alternative may be restated in the following form a nonzero is either an eigenvalue of K, or it lies in the domain of the resolvent ...
Famous quotes containing the word alternative:
“If English is spoken in heaven ... God undoubtedly employs Cranmer as his speechwriter. The angels of the lesser ministries probably use the language of the New English Bible and the Alternative Service Book for internal memos.”
—Charles, Prince Of Wales (b. 1948)