Diagonalization transformation

The C-conditions ascertain the validity of the intermediate normalization, Eq. (6), by requiring that the off-diagonal transformed coefficients c that are associated with the reference configurations ] j), (j i) in the target wave function must vanish, since... 

The transformation matrix is seen to be diagonal. Thus in forming linear combinations of ipi, 2 > 3 > and which are to have a diagonal transformation matrix, we must combine ipi with or ip2 with. ... 

Suppose that we have two different illuminants. Each illuminant defines a local coordinate system inside the three- dimensional space of receptors as shown in Figure 3.23. A diagonal transform, i.e. a simple scaling of each color channel, is not sufficient to align the coordinate systems defined by the two illuminants. A simple scaling of the color channels can only be used if the response functions of the sensor are sufficiently narrow band, i.e. they can be approximated by a delta function. 

Figure 3.23 Two different illuminants define two coordinate systems within the space of receptors. A simple diagonal transform, i.e. scaling of the color channels, is not sufficient to align the two coordinate systems.

In order to obtain an output image that is corrected for the color of the illuminant we only need to divide each channel by L,. The output image will then appear to have been taken under a white light. This can be done by applying a diagonal transform. Let S be a diagonal... 

Finlayson GD, Drew MS and Funt BV 1994a Color constancy generalized diagonal transforms suffice. Journal of the Optical Society of America A 11(11), 3011-3019. 

These regression vectors are then assembled to form the banded diagonal transformation matrix, F, where p is the number of response values to be converted. 

Since the tensor P(s), Eq. 5, is numerically invariant with respect to a parallel translation of the general reference system ra, the diagonalizing transformation T(s) is likewise independent of such a translation. 

In classical systems spatial inversion symmetry can be considered completely independent of time. In three dimensions it may refer to inversion through a plane (mirror reflection), a line, or a point (centre), represented by diagonal transformation matrices such as... 

Relation Between Eigenvectors and Diagonalization Transformations Appendix B Coherent States in the Floquet Representation... 

Consider now two qubits transformations in Hilbert space. Since all diagonal matrices commute, for all diagonal transformation in space Fk Z Fj we... 

DIAGONALIZE TRANSFORMED FOCK MATRIX CALL DIAG(FPRIME.CPRIME.E)... 

If a transformation D is linear and it is also a change of scale, then D is a change of the unit of measure. This is equivalent to saying that D is a positive definite diagonal transformation. Time) transformation of equation (4.34) is defined by a diffeomorphism... 

We now turn our attention to the construction of /Jtrana. the reducible representation of the translational displacements at the /J-point, with q = (Tr/aXy -f / -f ). iitrans IS given in Table A-VII. The results for E, 3U and C3 follow immediately from the foregoing discussion. Only I needs some attention. We have already seen that the diagonal transformation coefficients Q,(iS) contribute —1 to the diagonal for each Uj(qk). We must, however, here investigate the factor yj.(iS, q) [Eq. (A.7)]. For the iJ-point, we obtain for I... 

It is also shown that a kinetic equation remains a kinetic one if transformed by a positive definite diagonal transformation /change of scale/ and any natural transformation of time does not change the presence or absence of negative cross-effects. 

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