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- Rotation_matrix abstract "In linear algebra, a rotation matrix is a matrix that is used to perform a rotation in Euclidean space. For example the matrixrotates points in the xy-Cartesian plane counter-clockwise through an angle θ 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.Rotation matrices also provide a means of numerically representing an arbitrary rotation of the axes about the origin, without appealing to angular specification. These coordinate rotations are a natural way to express the orientation of a camera, or the attitude of a spacecraft, relative to a reference axes-set. Once an observational platform's local X-Y-Z axes are expressed numerically as three direction vectors in world coordinates, they together comprise the columns of rotation matrix R (world --> platform) that transforms directions (expressed in world coordinates) into equivalent directions expressed in platform-local coordinates.The examples in this article apply to rotation of vectors anti-clockwise in a right-handed system by pre-multiplication. If any one of these is changed (e.g. rotating axes instead of vectors), then the transpose of the example matrix should be used.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).".
- Rotation_matrix thumbnail Counterclockwise_rotation.png?width=300.
- Rotation_matrix wikiPageExternalLink ansi.altervista.org.
- Rotation_matrix wikiPageExternalLink pg=1130.
- Rotation_matrix wikiPageExternalLink 0043d03ee1c1013c85256bfa0067f5a6?OpenDocument.
- Rotation_matrix wikiPageExternalLink RotationMatrix.html.
- Rotation_matrix wikiPageExternalLink search.jsp.
- Rotation_matrix wikiPageExternalLink scholar?hl=en&lr=&q=author%3AHigham+intitle%3AApplications+of+Matrix+Theory&as_publication=&as_ylo=1989&as_yhi=1989&btnG=Search.
- Rotation_matrix wikiPageExternalLink scholar?hl=en&lr=&q=author%3AWedderburn+intitle%3ALectures+on+Matrices&as_publication=&as_ylo=1934&as_yhi=1934&btnG=Search.
- Rotation_matrix wikiPageExternalLink pp077-081-Paeth-1986.pdf.
- Rotation_matrix wikiPageExternalLink aroundPoint.
- Rotation_matrix wikiPageExternalLink www.graphicsgems.org.
- Rotation_matrix wikiPageExternalLink pageviewer-idx?c=umhistmath;cc=umhistmath;rgn=full%20text;idno=ABS3153.0001.001;didno=ABS3153.0001.001;view=image;seq=00000349.
- Rotation_matrix wikiPageExternalLink 2000-201.html.
- Rotation_matrix wikiPageExternalLink lpr.
- Rotation_matrix wikiPageExternalLink plane-rotate.html.
- Rotation_matrix wikiPageExternalLink kmath593.htm.
- Rotation_matrix wikiPageExternalLink issue11.
- Rotation_matrix wikiPageID "856005".
- Rotation_matrix wikiPageRevisionID "606615576".
- Rotation_matrix hasPhotoCollection Rotation_matrix.
- Rotation_matrix id "p/r082620".
- Rotation_matrix title "Rotation".
- Rotation_matrix subject Category:Matrices.
- Rotation_matrix subject Category:Transformation_(function).
- Rotation_matrix type Abstraction100002137.
- Rotation_matrix type Arrangement107938773.
- Rotation_matrix type Array107939382.
- Rotation_matrix type Group100031264.
- Rotation_matrix type Matrices.
- Rotation_matrix type Matrix108267640.
- Rotation_matrix comment "In linear algebra, a rotation matrix is a matrix that is used to perform a rotation in Euclidean space. For example the matrixrotates points in the xy-Cartesian plane counter-clockwise through an angle θ 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.".
- Rotation_matrix label "Drehmatrix".
- Rotation_matrix label "Matrice de rotation".
- Rotation_matrix label "Matriz de rotación".
- Rotation_matrix label "Matriz de rotação".
- Rotation_matrix label "Rotatiematrix".
- Rotation_matrix label "Rotation matrix".
- Rotation_matrix label "Матрица поворота".
- Rotation_matrix label "مصفوفة دوران".
- Rotation_matrix label "回転行列".
- Rotation_matrix label "旋转矩阵".
- Rotation_matrix sameAs Drehmatrix.
- Rotation_matrix sameAs Matriz_de_rotación.
- Rotation_matrix sameAs Biraketa_matrize.
- Rotation_matrix sameAs Matrice_de_rotation.
- Rotation_matrix sameAs 回転行列.
- Rotation_matrix sameAs Rotatiematrix.
- Rotation_matrix sameAs Matriz_de_rotação.
- Rotation_matrix sameAs m.03hn6d.
- Rotation_matrix sameAs Q1256564.
- Rotation_matrix sameAs Q1256564.
- Rotation_matrix sameAs Rotation_matrix.
- Rotation_matrix wasDerivedFrom Rotation_matrix?oldid=606615576.
- Rotation_matrix depiction Counterclockwise_rotation.png.
- Rotation_matrix isPrimaryTopicOf Rotation_matrix.
