However, instead of discarding equations corresponding to non-contributing individuals, these were never set up: the system was simply collapsed by changing the appropriate coordinates, i.e., by removing null rows and null columns.
The parity operation is like reflecting something in a mirror; it involves changing the coordinates (x, y, z) of each point to the "mirror" coordinates (−x, −y, −z).
Furthermore, the chlorine ions may reduce the formation of BiVO4 by changing the composition or coordinating structure of the growing unit; consequently, the crystallization process becomes slower and easier to control.
In this category, the precise position can be determined by changing the x or y coordinates.
The reflection itself can be carried out by changing the sign of one coordinate for all landmarks (e.g. all x coordinates).
Following [ 13] a multivariate equivalent of FA1 (i.e., the "unsigned" left-right differences) was defined by changing the signs of all coordinate differences (from left-right to right-left) whenever the inner product (also referred to as the dot product) of a left-right difference vector with the vector of mean left-right difference was negative.
For each specimen, a reflected copy of the original configuration of landmarks is produced (e.g. by changing the signs for one of the coordinates of all landmarks).
An anthropometric mask was nonrigidly mapped onto the original images and their reflections [ 15], which were constructed by changing the sign of the x-coordinate [ 22, 23].
The unnecessary increase of resolution at smaller radius typically brought about by polar coordinates, with its consequent stability limitations, is avoided by changing the number of azimuthal Fourier modes with the radial coordinate itself.
Change the symptoms by changing the cause.
