RM02
Orthogonal Matrix ( Rotation Matrix )
An nxn matrix is called orthogonal matrix if ATA = A AT = I
Determinant of orthogonal matrix is always +1 or –1.
Orthogonal matrix is always invertible. With its inverse = AT.
Geometrically Orthogonal matrices represent rotation ( rotational transformation ) with change in length of vector, i.e., if we premultiply a vector with orthogonal matrix then the resulting vector will be a rotated version of original vector.
The orthogonal matrix is called proper if its determinant is equal to 1.
A proper orthogonal matrix represents pure rotation.
The orthogonal matrix is called improper if its determinant is equal to –1.
An improper orthogonal matrix represents rotation with inversion ( reflection about origin ).
The columns of orthogonal matrix are orthonormal vectors.
The rows of orthogonal matrix are orthonormal vectors.
This video is uploaded by
Alpha Academy, Udaipur
[ Ссылка ]
Minakshi Porwal (9460189461)
![](https://s2.save4k.ru/pic/cESUIsMhpqI/mqdefault.jpg)