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.

Read more about Fredholm Alternative: Linear Algebra, Integral Equations, Functional Analysis

### Other articles related to "fredholm alternative, fredholm":

**Fredholm Alternative**- Functional Analysis - Alternative

... 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)