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...

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...

group of n × n orthogonal matrices, where the group operation is given by matrix multiplication (an orthogonal matrix is a real matrix whose inverse equals...

B]\,.\end{aligned}}} The matrix exponential of a skew-symmetric matrix A {\displaystyle A} is then an orthogonal matrix R {\displaystyle R} : R = exp...

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...

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...

orthogonal matrix is either +1 or −1. The special orthogonal group SO ⁡ ( n ) {\displaystyle \operatorname {SO} (n)} consists of the n × n orthogonal...

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...

any symmetric matrix whose entries are real can be diagonalized by an orthogonal matrix. More explicitly: For every real symmetric matrix A {\displaystyle...

finite-dimensional spaces, the matrix representation (with respect to an orthonormal basis) of an orthogonal transformation is an orthogonal matrix. Its rows are mutually...