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...

Householder transformations are unitary matrices, and since the multiplication of unitary matrices is itself a unitary matrix, this gives us the unitary matrix...

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

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

rotations, reflections, and the Fourier operator. Unitary operators generalize unitary matrices. Unitary operators are usually taken as operating on a Hilbert...

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)...

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

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

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...

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

{\displaystyle \mathbb {R} ^{k}.} A real unitary matrix is an orthogonal matrix, which describes a rigid transformation (an isometry of Euclidean space R k...

operators in the others. The interaction picture is a special case of unitary transformation applied to the Hamiltonian and state vectors. Haag's theorem says...

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...

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

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

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

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

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

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....

In quantum physics, unitarity is (or a unitary process has) the condition that the time evolution of a quantum state according to the Schrödinger equation...

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

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...

interferometer is described by an N×N unitary matrix U , {\displaystyle U,} which performs a linear transformation of the creation (annihilation) operators...

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

combinations of the delocalized orbitals, given by an appropriate unitary transformation. In the methane molecule, ab initio calculations show bonding character...

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

{\tilde {\Omega }}} terms are called counter-rotating consider a unitary transformation to the interaction or Dirac picture where the transformed Hamiltonian...

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

(metaplectic) unitary transformation. In particular, the time evolution symplectomorphism generated by the classical Hamiltonian deforms to a unitary transformation...