Geometric transformation

<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, a geometric transformation is any <a href="/facts/Bijection/j4gTuTmW">bijection</a> of a <a href="/facts/Set_(mathematics)/BfucfHMq">set</a> to itself (or to another such set) with some salient <a href="/facts/Geometry/wTQf5ffQ">geometrical</a> underpinning, such as preserving distances, angles, or ratios (scale). More specifically, it is a <a href="/facts/Function_(mathematics)/CdReEKCh">function</a> whose <a href="/facts/Domain_of_a_function/FQvoeUpX">domain</a> and <a href="/facts/Range_of_a_function/66CeTV6u">range</a> are sets of points – most often a <a href="/facts/Real_coordinate_space/tEtvw03F">real coordinate space</a>, 
  
    
      
        
          
            R
          
          
            2
          
        
      
    
    {\displaystyle \mathbb {R} ^{2}}
  
 or 
  
    
      
        
          
            R
          
          
            3
          
        
      
    
    {\displaystyle \mathbb {R} ^{3}}
  
 – such that the function is bijective so that its <a href="/facts/Inverse_function/Tg5nnXlu">inverse</a> exists. The study of geometry may be approached by the study of these transformations, such as in <a href="/facts/Transformation_geometry/fm0XUxv5">transformation geometry</a>.
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Geometric transformation open-in-new

Geometric transformation