[edit] Linear transformations, ranks and transpose
Main article: Transformation matrix
Main article: Transpose ...
# Linear transformation from XY to UTM coordinates: # 4 maps corners defined # UL NW # UR NE # LR SW # LL SE -584 585 598000 4920770 580 585 598020 4920770 580 -600 598020 4920750 -584 -600 598000 4920750 ...
Projection is a non-linear transformation, so that projections of the straight line segments implied by the internal representations of curves and polygons should produce curves. However, they only produce straight segments.
If there is a fixed point, we can take that as the origin, and the affine transformation reduces to a linear transformation. This may make it easier to classify and understand the transformation.
The images can have linear transformations applied, such as Move, Scale, Rotate, or Mirror, or more complex adjustments can be made using the register and warp tools.
For example, in ArcView, this is done through a World File which contains 6 parameters to provide a linear transform to display the image at the right location.
Affine transformation - A combination of linear transformations (rotation and scaling) followed by translation (shift of position). In geographic data processing, affine transformation is used to register maps of different scales and origins.
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for every subregion of , where is the -dimensional measure of . A linear transformation is area-preserving if its corresponding determinant has absolute value 1.
SEE ALSO: Conformal Mapping, Special Affine Transformation, Symplectic Map
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 See also: Transform, Transformation, Coordinate, Image, Area
  
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