For other uses, see Transformation (mathematics) (disambiguation).
In mathematics, a unitary transformation is a linear isomorphism that preserves the inner product: the inner product of two vectors before the transformation is equal to their inner product after the transformation.
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mathematics, a unitarytransformation is a linear isomorphism that preserves the inner product: the inner product of two vectors before the transformation is equal...
, as stated earlier. An N {\textstyle N} -by- N {\textstyle N} unitarytransformation U {\textstyle U} satisfies U U ∗ = I {\textstyle UU^{*}=I} . Taking...
functional analysis, a unitary operator is a surjective bounded operator on a Hilbert space that preserves the inner product. Unitary operators are usually...
circuit. One way to do this is to factor the matrix that encodes the unitarytransformation into a product of tensor products (i.e. series and parallel circuits)...
rotation, reflection or rotoreflection. In other words, it is a unitarytransformation. The set of n × n orthogonal matrices, under multiplication, forms...
operators in the others. The interaction picture is a special case of unitarytransformation applied to the Hamiltonian and state vectors. Operators and state...
theory. Two unitary representations π1: G → U(H1), π2: G → U(H2) are said to be unitarily equivalent if there is a unitarytransformation A:H1 → H2 such...
The quantum operation formalism describes not only unitary time evolution or symmetry transformations of isolated systems, but also the effects of measurement...
theory of solids. Wiley. ISBN 0-471-62412-8. Wagner, M. (1986). UnitaryTransformations in Solid State Physics. Elsevier Science. ISBN 0-444-86975-1....
Unlike the Eq.1 definition, the Fourier transform is no longer a unitarytransformation, and there is less symmetry between the formulas for the transform...
conical intersection, these terms are substantive. Therefore one unitarytransformation is performed from the adiabatic representation to the so-called...
{\displaystyle \mathbb {R} ^{k}} . A real unitary matrix is an orthogonal matrix, which describes a rigid transformation (an isometry of Euclidean space R k...
matrix h is positive semidefinite, it can be diagonalized with a unitarytransformation u: u † h u = [ γ 1 0 ⋯ 0 0 γ 2 ⋯ 0 ⋮ ⋮ ⋱ ⋮ 0 0 ⋯ γ N 2 − 1 ] {\displaystyle...
unit-phase factor. In general, the SVD is unique up to arbitrary unitarytransformations applied uniformly to the column vectors of both U {\displaystyle...
Wigner's theorem, this transformation of P H {\displaystyle \mathrm {P} {\mathcal {H}}} comes from a unitary or anti-unitarytransformation U ( g ) {\displaystyle...
\lambda _{k}+\lambda _{l}>0} . When the observable generates a unitarytransformation of the system with a parameter θ {\displaystyle \theta } from initial...
the quantum Fourier transform follow from the fact that it is a unitarytransformation. This can be checked by performing matrix multiplication and ensuring...
combinations of the delocalized orbitals, given by an appropriate unitarytransformation. In the methane molecule, ab initio calculations show bonding character...
transformed into the localized or fully delocalized descriptions via a unitarytransformation. Two different explanations for the nature of double and triple...
^{*}} With unitary normalization constants 1 / N {\textstyle 1/{\sqrt {N}}} , the DFT becomes a unitarytransformation, defined by a unitary matrix: U...
one-parameter group of unitarytransformations on the Hilbert space of states, and physical symmetries are realized by unitarytransformations. (It is possible...
settling on any unitary representation of the gammas is final, provided the spinor is transformed according to the unitarytransformation that corresponds...
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