# Category: Unitary operators

Fourier operator
The Fourier operator is the kernel of the Fredholm integral of the first kind that defines the continuous Fourier transform, and is a two-dimensional function when it corresponds to the Fourier transf
Shift operator
In mathematics, and in particular functional analysis, the shift operator also known as translation operator is an operator that takes a function x ↦ f(x)to its translation x ↦ f(x + a). In time serie
Russo–Dye theorem
In mathematics, the Russo–Dye theorem is a result in the field of functional analysis. It states that in a unital C*-algebra, the closure of the convex hull of the unitary elements is the closed unit
Dilation (operator theory)
In operator theory, a dilation of an operator T on a Hilbert space H is an operator on a larger Hilbert space K, whose restriction to H composed with the orthogonal projection onto H is T. More formal
Unitary operator
In functional analysis, a unitary operator is a surjective bounded operator on a Hilbert space that preserves the inner product. Unitary operators are usually taken as operating on a Hilbert space, bu
Unitary matrix
In linear algebra, a complex square matrix U is unitary if its conjugate transpose U* is also its inverse, that is, if where I is the identity matrix. In physics, especially in quantum mechanics, the
Fourier transform
A Fourier transform (FT) is a mathematical transform that decomposes functions into frequency components, which are represented by the output of the transform as a function of frequency. Most commonly
Rotation (mathematics)
Rotation in mathematics is a concept originating in geometry. Any rotation is a motion of a certain space that preserves at least one point. It can describe, for example, the motion of a rigid body ar
Discrete Fourier transform
In mathematics, the discrete Fourier transform (DFT) converts a finite sequence of equally-spaced samples of a function into a same-length sequence of equally-spaced samples of the discrete-time Fouri