Active and Passive Transformation - Example

Example

As an example, in the vector space ℝ2, let {e1,e2} be a basis, and consider the vector v = v1e1 + v2e2. A rotation through angle θ is given by the matrix:

R= \begin{pmatrix} \cos \theta & -\sin \theta\\ \sin \theta & \cos \theta \end{pmatrix},

which can be viewed either as an active transformation or a passive transformation, as described below.

Read more about this topic:  Active And Passive Transformation

Famous quotes containing the word example:

    “Our intellect is not the most subtle, the most powerful, the most appropriate, instrument for revealing the truth. It is life that, little by little, example by example, permits us to see that what is most important to our heart, or to our mind, is learned not by reasoning but through other agencies. Then it is that the intellect, observing their superiority, abdicates its control to them upon reasoned grounds and agrees to become their collaborator and lackey.”
    —Marcel Proust (1871–1922)