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- Orthogonal_matrix abstract "In linear algebra, an orthogonal matrix is a square matrix with real entries whose columns and rows are orthogonal unit vectors (i.e., orthonormal vectors), i.e.where I is the identity matrix. This leads to the equivalent characterization: a matrix Q is orthogonal if its transpose is equal to its inverse:An orthogonal matrix Q is necessarily invertible (with inverse Q−1 = QT), unitary (Q−1 = Q*) and therefore normal (Q*Q = QQ*) in the reals. The determinant of any orthogonal matrix is either +1 or −1. As a linear transformation, an orthogonal matrix preserves the dot product of vectors, and therefore acts as an isometry of Euclidean space, such as a rotation or reflection. In other words, it is a unitary transformation.The set of n × n orthogonal matrices forms a group O(n), known as the orthogonal group. The subgroup SO(n) consisting of orthogonal matrices with determinant +1 is called the special orthogonal group, and each of its elements is a special orthogonal matrix. As a linear transformation, every special orthogonal matrix acts as a rotation.The complex analogue of an orthogonal matrix is a unitary matrix.".
- Orthogonal_matrix wikiPageExternalLink etna.mcs.kent.edu.
- Orthogonal_matrix wikiPageExternalLink art_0907079.html.
- Orthogonal_matrix wikiPageExternalLink art_0911038.html.
- Orthogonal_matrix wikiPageExternalLink MatrixOrthogonal.html.
- Orthogonal_matrix wikiPageExternalLink pap-mf.html.
- Orthogonal_matrix wikiPageID "105620".
- Orthogonal_matrix wikiPageRevisionID "604213544".
- Orthogonal_matrix hasPhotoCollection Orthogonal_matrix.
- Orthogonal_matrix id "p/o070320".
- Orthogonal_matrix title "Orthogonal matrix".
- Orthogonal_matrix subject Category:Matrices.
- Orthogonal_matrix type Abstraction100002137.
- Orthogonal_matrix type Arrangement107938773.
- Orthogonal_matrix type Array107939382.
- Orthogonal_matrix type Group100031264.
- Orthogonal_matrix type Matrices.
- Orthogonal_matrix type Matrix108267640.
- Orthogonal_matrix comment "In linear algebra, an orthogonal matrix is a square matrix with real entries whose columns and rows are orthogonal unit vectors (i.e., orthonormal vectors), i.e.where I is the identity matrix. This leads to the equivalent characterization: a matrix Q is orthogonal if its transpose is equal to its inverse:An orthogonal matrix Q is necessarily invertible (with inverse Q−1 = QT), unitary (Q−1 = Q*) and therefore normal (Q*Q = QQ*) in the reals.".
- Orthogonal_matrix label "Macierz ortogonalna".
- Orthogonal_matrix label "Matrice orthogonale".
- Orthogonal_matrix label "Matrice ortogonale".
- Orthogonal_matrix label "Matriz ortogonal".
- Orthogonal_matrix label "Matriz ortogonal".
- Orthogonal_matrix label "Orthogonal matrix".
- Orthogonal_matrix label "Orthogonale Matrix".
- Orthogonal_matrix label "Orthogonale matrix".
- Orthogonal_matrix label "Ортогональная матрица".
- Orthogonal_matrix label "مصفوفة متعامدة".
- Orthogonal_matrix label "正交矩阵".
- Orthogonal_matrix label "直交行列".
- Orthogonal_matrix sameAs Ortogonální_matice.
- Orthogonal_matrix sameAs Orthogonale_Matrix.
- Orthogonal_matrix sameAs Ορθογώνιος_πίνακας.
- Orthogonal_matrix sameAs Matriz_ortogonal.
- Orthogonal_matrix sameAs Matrize_ortogonal.
- Orthogonal_matrix sameAs Matrice_orthogonale.
- Orthogonal_matrix sameAs Matrice_ortogonale.
- Orthogonal_matrix sameAs 直交行列.
- Orthogonal_matrix sameAs 직교행렬.
- Orthogonal_matrix sameAs Orthogonale_matrix.
- Orthogonal_matrix sameAs Macierz_ortogonalna.
- Orthogonal_matrix sameAs Matriz_ortogonal.
- Orthogonal_matrix sameAs m.0qh1r.
- Orthogonal_matrix sameAs Q333871.
- Orthogonal_matrix sameAs Q333871.
- Orthogonal_matrix sameAs Orthogonal_matrix.
- Orthogonal_matrix wasDerivedFrom Orthogonal_matrix?oldid=604213544.
- Orthogonal_matrix isPrimaryTopicOf Orthogonal_matrix.