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Matrix norm; Spectral radius; Normed division algebra; Stone–Weierstrass theorem; Banach algebra *-algebra; B*-algebra; C*-algebra. Universal C*-algebra; Spectrum of a C*-algebra; Positive element; Positive linear functional; operator algebra. nest algebra; reflexive operator algebra; Calkin algebra; Gelfand representation; Gelfand–Naimark ...
Functional principal component analysis (FPCA) is a statistical method for investigating the dominant modes of variation of functional data. Using this method, a random function is represented in the eigenbasis, which is an orthonormal basis of the Hilbert space L 2 that consists of the eigenfunctions of the autocovariance operator .
In linear algebra and functional analysis, a projection is a linear transformation from a vector space to itself (an endomorphism) such that =. That is, whenever P {\displaystyle P} is applied twice to any vector, it gives the same result as if it were applied once (i.e. P {\displaystyle P} is idempotent ).
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.
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.
In functional analysis, the open mapping theorem, also known as the Banach–Schauder theorem or the Banach theorem [1] (named after Stefan Banach and Juliusz Schauder), is a fundamental result that states that if a bounded or continuous linear operator between Banach spaces is surjective then it is an open map.
This is an example of a non-linear functional. The Riemann integral is a linear functional on the vector space of functions defined on [a, b] that are Riemann-integrable from a to b. In mathematics, a functional is a certain type of function. The exact definition of the term varies depending on the subfield (and sometimes even the author).
Among others, Zwicky applied morphological analysis to astronomical studies and jet and rocket propulsion systems. As a problem-structuring and problem-solving technique, morphological analysis was designed for multi-dimensional, non-quantifiable problems where causal modelling and simulation do not function well, or at all.