Assertion: orthogonal matrix | /r/HasProperty | pure rotation
Facets:
value: as a linear transformation
type: MANNER
value: without reflection
type: OTHER
Source sentences:
text: As a linear transformation, every orthogonal matrix with determinant +1 is a pure rotation without reflection, i.e., the transformation preserves the orientation of the transformed structure, while every orthogonal matrix with determinant -1 reverses the orientation, i.e., is a composition of a pure reflection and a (possibly null) rotation.
text: As a linear transformation, every orthogonal matrix with determinant +1 is a pure rotation, while every orthogonal matrix with determinant −1 is either a pure reflection, or a composition of reflection and rotation.
text: As a linear transformation, every orthogonal matrix with determinant +1 is a pure rotation, while every orthogonal matrix with determinant −1 is either a pure reflection, or a composition of reflection and rotation.