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.




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Minakshi Porwal (9460189461)

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