Difference between revisions of "Symmetric matrix"
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:''A'' = ''A<sup>T</sup>'' | :''A'' = ''A<sup>T</sup>'' | ||
| + | |||
| + | Thus the entries of A satisfy: <math>a_{ij} = a_{ji}</math>. | ||
Symmetric matrices have useful characteristics: | Symmetric matrices have useful characteristics: | ||
Revision as of 01:34, June 20, 2011
A symmetric matrix is a square matrix that equals its transpose:
- A = AT
Thus the entries of A satisfy: .
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.