Rotation matrices

camchetan

Show that a rotation by θ followed by a rotation by φ can be expressed as either
two consecutive rotations, or one rotation of (θ + φ). That is, show that Qθ Qφ = Qθ+φ, where Q is the rotation matrix.

Can any one answer this question I'm a beginner in Linear Algebra

micromass

What is the rotation matrix with angle [itex]\theta[/itex]??

genericusrnme

do the matrix multiplication and see what happens

HallsofIvy

You will need the trig identities [itex]cos(\theta+ \phi)= cos(\theta)cos(\phi)- sin(\theta)sin(\phi)[/itex] and [itex]sin(\theta+ \phi)= sin(\theta)cos(\phi)+ cos(\theta)sin(\phi)[/itex]