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Rotation matrix
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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 counter-clockwise through an angle ? about the origin of the Cartesian coordinate system. To perform the rotation using a rotation matrix R, the position of each point must be represented by a column vector v, containing the coordinates of the point. A rotated vector is obtained by using the matrix multiplication Rv. Since matrix multiplication has no effect on the zero vector (the coordinates of the origin), rotation matrices can only be used to describe rotations about the origin of the coordinate system. Rotation matrices provide an algebraic description of such rotations, and are used extensively for computations in geometry, physics, and computer graphics.Rotation matrices are square matrices, with real entries. More specifically they can be characterized as orthogonal matrices with determinant 1::.In some literature, the term rotation is generalized to include improper rotations, characterized by orthogonal matrices with determinant -1 (instead of +1). These combine proper rotations with reflections (which invert orientation). In other cases, where reflections are not being considered, the label proper may be dropped. This convention is followed in this article.The set of all orthogonal matrices of size n with determinant +1 forms a group known as the special orthogonal group SO(n). The set of all orthogonal matrices of size n with determinant +1 or -1 forms the (general) orthogonal group O(n).
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Created By:
System
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