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Singular value (or S-number) Fredholm operator; Fuglede's theorem; Compression (functional analysis) Friedrichs extension; Stone's theorem on one-parameter unitary groups; Stone–von Neumann theorem; Functional calculus. Continuous functional calculus; Borel functional calculus; Hilbert–Pólya conjecture
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (for example, inner product, norm, or topology) and the linear functions defined on these spaces and suitably respecting these structures.
Add the following into the article's bibliography * {{Rudin Walter Functional Analysis|edition=2}} and then add a citation by using the markup Some sentence in the body of the article.{{sfn | Rudin | 1991 | pp=1-2}} which results in: Some sentence in the body of the article. [1]
Functional Analysis. International Series in Pure and Applied Mathematics. Vol. 8 (Second ed.). New York, NY: McGraw-Hill Science/Engineering/Math. ISBN 978-0-07-054236-5. OCLC 21163277. M. Takesaki, Theory of Operator Algebras I, Springer, 2001, 2nd printing of the first edition 1979. Yoshida, Kôsaku (1980), Functional Analysis (sixth ed ...
Add the following into the article's bibliography * {{Lax Functional Analysis}} and then add a citation by using the markup Some sentence in the body of the article.{{sfn|Lax|2002|pp=1-2}} which results in: Some sentence in the body of the article. [1]
The Frobenius norm defined by ‖ ‖ = = = | | = = = {,} is self-dual, i.e., its dual norm is ‖ ‖ ′ = ‖ ‖.. The spectral norm, a special case of the induced norm when =, is defined by the maximum singular values of a matrix, that is, ‖ ‖ = (), has the nuclear norm as its dual norm, which is defined by ‖ ‖ ′ = (), for any matrix where () denote the singular values ...
In functional analysis, a branch of mathematics, it is sometimes possible to generalize the notion of the determinant of a square matrix of finite order (representing a linear transformation from a finite-dimensional vector space to itself) to the infinite-dimensional case of a linear operator S mapping a function space V to itself.
In mathematics, particularly in functional analysis, the spectrum of a bounded linear operator (or, more generally, an unbounded linear operator) is a generalisation of the set of eigenvalues of a matrix.