Chapter 7- Linear transformations Flashcards
Linear transformation properties
Maps origin onto itself
Representable by a matrix
Reflection in y axis
(-1 0)
(0 1)
Reflection in x axis
(1 0)
(0 -1)
Reflection y=x
(0 1)
(1 0)
Reflection in y=-x
(0 -1)
(-1 0)
Rotation angle θ anticlockwise about origin
(cosθ -sinθ)
(sinθ cosθ)
Stretch of scale factor a along x axis and stretch of scale factor b along y axis
(a 0)
(0 b)
What does detM for a matrix representing a linear transformation show?
The area scale factor
Reflection in x=0 plane
(-1 0 0)
(0 1 0)
(0 0 1)
Reflection in y=0 plane
(1 0 0)
(0 -1 0)
(0 0 1)
Reflection in z=0 plane
(1 0 0)
(0 1 0)
(0 0 -1)
Rotation by θ about x axis
(1 0 0)
(0 cosθ -sinθ)
(0 sinθ cosθ)
Rotation by θ about y axis
(cosθ 0 sinθ)
(0 1 0 )
(-sinθ 0 cosθ)
Rotation by θ about z axis
(cosθ -sinθ 0)
(sinθ cosθ 0)
(0 0 1)