imaginary rotation

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• Imaginary time — in quantum mechanics Imaginary time is a concept derived from quantum mechanics and is essential in connecting quantum mechanics with statistical mechanics. Imaginary time scriptstyle au is obtained from real time via a Wick rotation by… …   Wikipedia

• Imaginary number — In mathematics, an imaginary number (or purely imaginary number) is a complex number whose squared value is a real number not greater than zero.Ahlfors, Lars V. Complex Analysis. 3rd Ed. New York: McGraw Hill, 1979. Pages 1 4.] The imaginary unit …   Wikipedia

• Imaginary unit — i in the complex or cartesian plane; real numbers fall on the horizontal axis, and imaginary numbers fall on the vertical axis In mathematics, the imaginary unit allows the real number system ℝ to be extended to the complex number system ℂ, which …   Wikipedia

• Rotation matrix — In linear algebra, a rotation matrix is a matrix that is used to perform a rotation in Euclidean space. For example the matrix rotates points in the xy Cartesian plane counterclockwise through an angle θ about the origin of the Cartesian… …   Wikipedia

• Rotation — This article is about movement of a physical body. For other uses, see Rotation (disambiguation). A polyhedron resembling a sphere rotating around an axis. A rotation is a circular movement of an object around a center (or point) of rotation. A… …   Wikipedia

• rotation axis — noun : a simple axis of symmetry in a crystal about which the whole crystal configuration is brought into coincidence with its original aspect by a rotation of one half, one third, one fourth, or one sixth of a turn about the axis * * * Crystall …   Useful english dictionary

• rotation axis — Crystall. an imaginary line through a crystal about which the crystal may be rotated a specified number of degrees and be brought back to its original position. Also called axis of symmetry, symmetry axis of rotation. Cf. symmetry element. [1900… …   Universalium

• Wick rotation — In physics, Wick rotation, named after Gian Carlo Wick, is a method of finding a solution to a problem in Minkowski space from a solution to a related problem in Euclidean space, by analytic continuation.It is motivated by the observation that… …   Wikipedia

• Quaternions and spatial rotation — Unit quaternions provide a convenient mathematical notation for representing orientations and rotations of objects in three dimensions. Compared to Euler angles they are simpler to compose and avoid the problem of gimbal lock. Compared to… …   Wikipedia

• Euler's rotation theorem — In kinematics, Euler s rotation theorem states that, in three dimensional space, any displacement of a rigid body such that a point on the rigid body remains fixed, is equivalent to a rotation about a fixed axis through that point. The theorem is …   Wikipedia

• Orientation (geometry) — This article is about the orientation or attitude of an object in space. For orientation as a property in linear algebra, see Orientation (vector space). Changing orientation of a rigid body is the same as rotating the axes of a reference frame… …   Wikipedia