General:

• The location of the origin
• The orientation of x and y axes
• The length of units along each axes

• Device Space - specific to output device
• User Space - device independent
  • X axis is horizontal, increases to right
  • Y axis is vertical, increases upward
  • the length of one unit defaults to 1/72".
• Text Space - used for defining coordinates of text
• Glyph Space - used for defining character glyphs
• Image Space - used to define sampled images
• Pattern Space - used to define patterns

A transformation matrix defines the relationship between two coordinate spaces. Generally, a transformation matrix is denoted as an array of six elements.

• Translation is denoted [1 0 0 1 Tx Ty]
• Scaling is donoted [Sx 0 0 Sy 0 0]
• Rotation is denoted [cos q sin q -sin q cos q 0 0], where q is the angle to rotate by. The angle is measured anti-clockwise.
• Skewing is denoted [1 tan A tan B 1 0 0], a is the x axis skew and B is the y axis skew.