|
|
|
|
|
Symmetric MatrixIn linear algebra, a symmetric matrix is a matrix that is its own transpose. Thus A is symmetric if: -
which implies that A is a square matrix. Examples The entries of a symmetric matrix are symmetric with respect to the main diagonal (top left to bottom right). Example: -
1 & 2 & 3\\ 2 & 0 & 5\\ 3 & 5 & 6\end{bmatrix} Any diagonal matrix is symmetric, since all its off-diagonal entries are zero. Properties One of the basic theorems concerning such matrices is the finite-dimensional spectral theorem, which says that any symmetric matrix whose entries are real can be diagonalized by an orthogonal matrix. This is a special case of a Hermitian matrix. See also skew-symmetric (or antisymmetric) matrix. Other types of symmetry or pattern in square matrices have special names: see for example:
|  | westport, new york willsboro, new york wilmington, new york altamont, franklin county, new york bangor, new york bellmont, new york bombay, new york brandon, new york brighton, franklin county, new york brushton, new york constable, new york
| dickinson, franklin county, new york football world cup 1998 duane, new york fort covington, new york franklin, franklin county, new york harrietstown, new york moira, new york santa clara, new york tupper lake, new york waverly, franklin county, new york westville, new york
| bleecker, new york caroga, new york ephratah, new york gloversville, new york northampton, fulton county, new york northville, fulton county, new york oppenheim, new york perth, new york stratford, new york alabama, new york bethany, new york
| byron, new york corfu, new york darien, new york pavilion, new york pembroke, new york stafford, new york ashland, greene county, new york durham, new york halcott, new york jefferson heights, new york jewett, new york
|
|
 |
|
| Copyright 2005-2009 OnPedia.com. All Rights Reserved |
|
|