mathematics, a unitary transformation is a linear isomorphism that preserves the inner product: the inner product of two vectors before the transformation is equal...

original. A unitary transformation (or frame change) can be expressed in terms of a time-dependent Hamiltonian H ( t ) {\displaystyle H(t)} and unitary operator...

, as stated earlier. An N {\textstyle N} -by- N {\textstyle N} unitary transformation U {\textstyle U} satisfies U U ∗ = I {\textstyle UU^{*}=I} . Taking...

another Transformation optics, generalized optical devices Unitary transformation (quantum mechanics) Transformation problem, in economics Transformation (linguistics)...

morphism Unitary operator Unitary transformation Unitary representation Unitarity (physics) E-unitary inverse semigroup Unitary authority Unitary state Unital...

In quantum mechanics, the Schrieffer–Wolff transformation is a unitary transformation used to determine an effective (often low-energy) Hamiltonian by...

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 unitary transformation into a product of tensor products (i.e. series and parallel circuits)...

rotation, reflection or rotoreflection. In other words, it is a unitary transformation. The set of n × n orthogonal matrices, under multiplication, forms...

The quantum operation formalism describes not only unitary time evolution or symmetry transformations of isolated systems, but also the effects of measurement...

theory. Two unitary representations π1: G → U(H1), π2: G → U(H2) are said to be unitarily equivalent if there is a unitary transformation A:H1 → H2 such...

)\end{bmatrix}}} Geometric transformation Improper rotation Linear transformation Orthogonal matrix Rigid transformation Unitary transformation Rowland, Todd. "Orthogonal...

operators in the others. The interaction picture is a special case of unitary transformation applied to the Hamiltonian and state vectors. Operators and state...

that is to be cloned, and applying a unitary transformation to the combined system. If the unitary transformation is chosen correctly, several components...

theory of solids. Wiley. ISBN 0-471-62412-8. Wagner, M. (1986). Unitary Transformations in Solid State Physics. Elsevier Science. ISBN 0-444-86975-1....

unit-phase factor. In general, the SVD is unique up to arbitrary unitary transformations applied uniformly to the column vectors of both ⁠ U {\displaystyle...

{\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 unitary transformation u: u † h u = [ γ 1 0 ⋯ 0 0 γ 2 ⋯ 0 ⋮ ⋮ ⋱ ⋮ 0 0 ⋯ γ N 2 − 1 ] {\displaystyle...

Unlike the Eq.1 definition, the Fourier transform is no longer a unitary transformation, and there is less symmetry between the formulas for the transform...

a unitary transformation, that is, the physics does not change under such a unitary basis transformation. Therefore, such a unitary transformation can...

\lambda _{k}+\lambda _{l}>0} . When the observable generates a unitary transformation of the system with a parameter θ {\displaystyle \theta } from initial...

has been recovered from the ancilla qubits using suitable local unitary transformation only in the environment Hilbert space in accordance with the no-hiding...

settling on any unitary representation of the gammas is final, provided the spinor is transformed according to the unitary transformation that corresponds...

one-parameter group of unitary transformations on the Hilbert space of states, and physical symmetries are realized by unitary transformations. (It is possible...

In American law, the unitary executive theory is a Constitutional law theory according to which the President of the United States has sole authority...

Wigner's theorem, this transformation of P H {\displaystyle \mathrm {P} {\mathcal {H}}} comes from a unitary or anti-unitary transformation U ( g ) {\displaystyle...

requires a special kind of reversible function, namely a unitary mapping, that is, a linear transformation of a complex inner product space that preserves the...

non-unitary transformation on a quantum system which maps pure states to mixed states. This is a non-unitary process because any transformation that...

transformed into the localized or fully delocalized descriptions via a unitary transformation. Two different explanations for the nature of double and triple...

2017. Chen, Xie; Gu, Zheng-Cheng; Wen, Xiao-Gang (2010). "Local unitary transformation, long-range quantum entanglement, wave function renormalization...