A transformation matrix is a matrix representing a linear transformation. If is a transformation from to , is the m×n transformation matrix of such that
The matrix can found by taking the column vectors representing the transformations of unit vectors in each direction. For example,
Therefore, the transformation matrix for will be
Which does indeed represent the transformation .
Common transformation matrices[]
[]
Identity transformation:
Projection onto -axis:
Projection onto -axis:
Reflection over
Reflection over -axis:
Reflection over -axis:
Stretch by factor
Vector projection onto :
Reflection over y=mx:
Rotation counterclockwise by :
Rotation clockwise by :