Difference between revisions of "Symmetric matrix"
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:''A'' = ''A<sup>T</sup>'' | :''A'' = ''A<sup>T</sup>'' | ||
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| + | Symmetric matrices have useful characteristics: | ||
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| + | :*if two matrices are similar to each other, then they have the same [[eigenvalue]]s | ||
| + | :*the eigenvectors of a symmetric matrix form an orthonormal basis | ||
| + | :*symmetric matrices are [[diagonalizable]]. | ||
[[Category:linear algebra]] | [[Category:linear algebra]] | ||
Revision as of 13:26, May 1, 2010
A symmetric matrix is a square matrix that equals its transpose:
- A = AT
Symmetric matrices have useful characteristics:
- if two matrices are similar to each other, then they have the same eigenvalues
- the eigenvectors of a symmetric matrix form an orthonormal basis
- symmetric matrices are diagonalizable.