"orientation" nach Englisch mit Beispielen - Kollokationen-Wörterbuch Englisch
- A matrix will preserve or reverse orientation according to whether the determinant of the matrix is positive or negative.
- Geometrically, this consists of all the elements of GL(n) that preserve both orientation and volume of the various geometric solids in Euclidean space.
- Rotations are direct isometries, i.e., isometries preserving orientation.
- Each of these groups has a subgroup of transformations which preserve orientation: those where the determinant of A is positive.
- Unlike in the three-dimensional case, we can equivalently restrict the affine transformations to those that preserve orientation.
- Those which preserve orientation are called proper, and as linear transformations they have determinant +1.
- In his book Principles of Mathematics (1903), Russell considered a motion to be a Euclidean isometry that preserves orientation.
- In addition to preserving length, proper rotations must also preserve orientation.
- Even though it appears to be a well-behaved function, it is not holomorphic; it reverses orientation whereas holomorphic functions locally preserve orientation.
- There is a subgroup E(n) of the direct isometries, i.e., isometries preserving orientation, also called rigid motions; they are the rigid body moves.
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