Moreover; in the IPPLEGA we took advantage of a proposed transformation matrix
The application of Algorithm 1 from  to Q yields the transformation matrix
where S([LAMBDA]) is a 4 x 4 matrix which depends only on the relative velocities of O and O' and [LAMBDA] is the Lorentz transformation matrix
. S ([LAMBDA]) has an inverse if O [right arrow] O' and also O' [right arrow] O.
in which Q is the transformation matrix
from the global to local coordinates.
[mathematical expression not reproducible] is the transformation matrix
from the rectangular to the inverted trapezoidal.
Next, this system calculates a transformation matrix
to convert the coordinates system whose origin is a set point to Senz3D coordinates system.
To retain the rotational invariance structure in the space-time beam-space, the conjugate centrosymmetric DFT matrix is applied as the transformation matrix
First, according to the joint angles measured by the absolute position sensor, the homogeneous transformation matrix
[sup.base][T.sub.end] between the end and the mounting base of the manipulator is calculated by the manipulator's forward kinematics.
The supersymmetrized versions of the bosonic quantities can be obtained by acting with the transformation matrix
where T is the standard (6 x 6) transformation matrix
. The corresponding concrete stresses, [[sigma].sub.123], are determined from equivalent uniaxial constitutive laws for axial and shear stresses (Figure 5(a)).
Then the homogeneous transformation matrix
is applied for representing geometric relations between cameras from different coordinate system.