Prove the Hamilton-Rodrigues theorem using the finite rotation formula.

Expert Solution

The rotation matrix for rotation about Z axis by a finite angle theta is

when this angle is 180 degrees or Pi radians, Cos(180 degrees) = -1, Sin(180 degrees) = 0. Therefore

Similarly, rotation matrix for rotation about X axis by a Pi radians is

and otation matrix for rotation about Y axis by Pi radians is

Hamilton Rodrigues theorem states that a sequence of rotation about three mutually perpendicular axes(X, Y and Z) by Pi radians is equivalent to the identity transformation. Hence

which is the identity matrix. Thus Hamilton-Rodrigues theorem is proved.

genius_generous answered 1 year ago

Using Kurosch's subgroup theorem for free proucts,prove that every finite subgroup of the free product of...

Using Kurosch's subgroup theorem for free proucts,prove that every finite subgroup of the free product of finite groups is isomorphic to a subgroup of some free factor.

Prove that the product of a rotation and a translation is a rotation.

Prove Descartes' circle theorem. (using trig)

Prove Taylor's Theorem (using n=3 case)

Using Picard’s Uniqueness Theorem or otherwise, prove the Existence and Uniqueness Theorem for a First Order...

Using Picard’s Uniqueness Theorem or otherwise, prove the Existence and Uniqueness Theorem for a First Order Linear Differential Equation.

prove that a compact set is closed using the Heine - Borel theorem

Prove Rolles Theorem

prove the Liouville's theorem?

Prove the Heine-Borel Theorem

Prove or Disprove The set of all finite strings is undecidable. The set of all finite...

Prove or Disprove The set of all finite strings is undecidable. The set of all finite strings is recognizable

Question