Orthogonal Matrix: Rotation or Refection

By Kardi Teknomo, PhD .

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Orthogonal Matrix Applications

Here is an interesting fact and application about orthogonal matrix: it is either a rotation matrix or a reflection matrix.

How to know if an orthogonal 2 by 2 matrix is a rotation matrix or a reflection matrix ?

Solution:

Check the determinant.
If the determinant is +1, then the orthogonal matrix is a rotation matrix.
If the determinant is -1, then the orthogonal matrix is a reflection matrix about 45 degree counterclockwise from x axis.

See also : Orthogonal matrix , Determinant

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