We have shown via a careful error analysis that it is possible to do this deflation via a structure preserving real orthogonal or unitary transformation
as well as with a Schur complement approach.
The second unitary transformation
is an inversion about average operation.
We make use of unitary transformation
discussed in previous studies  which render the most significant first order dipole moment to effect the Curie temperature ([T.
When anyons move around each other along braided paths, the motion changes the pattern of the anyons' interactions with each other--a change physicists call a unitary transformation
Any unitary transformation
of a quantum state space is a legitimate quantum transformation, and vice versa.
For example, the unitary transformation
that inverts the amplitude of each basis state is modeled as follows:
Although most of the unitary transformations
can only be implemented by approximation very inefficiently, that is the number of fault-tolerant gates is exponential in the number of qubits of the operator, it may be possible that some universal bases are more efficient than others to approximate some specific set of unitary operators.
Focusing mainly on the unitary transformations
, which the Fourier transform shares with other transforms that have been derived from it, they seek to help graduate students and engineers use new forms and methods of signals and images in the frequency domain, as well as in the so-called frequency-and-time domain.
The transformation theory of quantum mechanics shows how these different representations are related by unitary transformations
Background appendices are included on mathematical concepts, quantum measurement, the harmonic oscillator, and unitary transformations
For the transformation from the Cartesian OXYZ into the O'X'Y'Z' the following unitary transformations
have been used:
Furthermore, all the computations are carried out using unitary transformations
and, therefore, the algorithms are both fast and numerically robust.