In functional analysis, a unitary operator is a surjective bounded operator on a Hilbert space that preserves the inner product.Non-trivial examples include rotations, reflections, and the Fourier operator.Unitary operators generalize unitary matrices.Unitary operators are usually taken as operating on a Hilbert space, but the same notion serves to define the concept of isomorphism between Hilbert spaces.
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Unitary matrix in the context of Special unitary group
In mathematics, the special unitary group of degree n, denoted SU(n), is the Lie group of n Ă— n unitary matrices with determinant 1.
The matrices of the more general unitary group may have complex determinants with absolute value 1, rather than real 1 in the special case.
View the full Wikipedia page for Special unitary groupUnitary matrix in the context of Cabibbo–Kobayashi–Maskawa matrix
In the Standard Model of particle physics, the Cabibbo–Kobayashi–Maskawa matrix, CKM matrix, quark mixing matrix, or KM matrix is a unitary matrix that contains information on the strength of the flavour-changing weak interaction. Technically, it specifies the mismatch of quantum states of quarks when they propagate freely and when they take part in the weak interactions. It is important in the understanding of CP violation. This matrix was introduced for three generations of quarks by Makoto Kobayashi and Toshihide Maskawa, adding one generation to the matrix previously introduced by Nicola Cabibbo. This matrix is also an extension of the GIM mechanism, which only includes two of the three current families of quarks.
View the full Wikipedia page for Cabibbo–Kobayashi–Maskawa matrixUnitary matrix in the context of S-matrix
In physics, the S-matrix or scattering matrix is a matrix that relates the initial state and the final state of a physical system undergoing a scattering process. It is used in quantum mechanics, scattering theory and quantum field theory (QFT).
More formally, in the context of QFT, the S-matrix is defined as the unitary matrix connecting sets of asymptotically free particle states (the in-states and the out-states) in the Hilbert space of physical states: a multi-particle state is said to be free (or non-interacting) if it transforms under Lorentz transformations as a tensor product, or direct product in physics parlance, of one-particle states as prescribed by equation (1) below. Asymptotically free then means that the state has this appearance in either the distant past or the distant future.
View the full Wikipedia page for S-matrixUnitary matrix in the context of Unitary group
In mathematics, the unitary group of degree n, denoted U(n), is the group of n Ă— n unitary matrices, with the group operation of matrix multiplication. The unitary group is a subgroup of the general linear group GL(n, C), and it has as a subgroup the special unitary group, consisting of those unitary matrices with determinant 1.
In the simple case n = 1, the group U(1) corresponds to the circle group, isomorphic to the set of all complex numbers that have absolute value 1, under multiplication. All the unitary groups contain copies of this group.
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