In linear algebra, an orthogonal matrix, or orthonormal matrix, is a real square matrix whose columns and rows are orthonormal vectors. One way to express... 36 KB (4,802 words) - 22:52, 2 February 2024 |
AA*). The determinant of any orthogonal matrix is either +1 or −1. A special orthogonal matrix is an orthogonal matrix with determinant +1. As a linear... 106 KB (13,106 words) - 15:41, 8 May 2024 |
In linear algebra, a semi-orthogonal matrix is a non-square matrix with real entries where: if the number of columns exceeds the number of rows, then the... 2 KB (309 words) - 18:36, 12 August 2023 |
B]\,.\end{aligned}}} The matrix exponential of a skew-symmetric matrix A {\displaystyle A} is then an orthogonal matrix R {\displaystyle R} : R = exp... 18 KB (3,543 words) - 22:03, 30 October 2023 |
matrix U is special unitary if it is unitary and its matrix determinant equals 1. For real numbers, the analogue of a unitary matrix is an orthogonal... 10 KB (1,307 words) - 23:15, 10 May 2024 |
they can be characterized as orthogonal matrices with determinant 1; that is, a square matrix R is a rotation matrix if and only if RT = R−1 and det... 99 KB (15,019 words) - 04:42, 13 May 2024 |
orthogonal matrix is either +1 or −1. The special orthogonal group SO ( n ) {\displaystyle \operatorname {SO} (n)} consists of the n × n orthogonal... 16 KB (1,831 words) - 01:25, 27 April 2024 |
being normalized: a matrix that is slightly off may not be orthogonal any more and is harder to convert back to a proper orthogonal matrix. Quaternions also... 66 KB (11,503 words) - 03:18, 19 April 2024 |