Encyclopedia > Orthonormal matrix

  Article Content

Orthonormal matrix

In linear algebra, an orthonormal matrix is a (not necessarily square) matrix with real or complex entries whose columns, treated as vectors in Rn or Cn, are orthonormal with respect to the standard inner product of Rn or Cn.

This means that an n-by-k matrix G is orthonormal if and only if

<math>G^*G = I_k </math>

where G* denotes the conjugate transpose of G and Ik is the k-by-k identity matrix.

If the n-by-k matrix G is orthonormal, then kn. The real n-by-k orthonormal matrices are precisely the matrices that result from deleting n-k columns from an orthogonal matrix; the complex n-by-k orthonormal matrices are precisely the matrices that result from deleting n-k columns from an unitary matrix. In particular, unitary and orthogonal matrices are themselves orthonormal.



All Wikipedia text is available under the terms of the GNU Free Documentation License

 
  Search Encyclopedia

Search over one million articles, find something about almost anything!
 
 
  
  Featured Article
Kuru Kuru Kururin

... gold star for getting through the level without any accidents. Kururin was released in Japan and Europe but not in the United States. However, because the GBA has no ...

 
 
 
This page was created in 23.7 ms