Symmetric matrix
This is the current revision of Symmetric matrix as edited by DavidB4-bot (talk | contribs) at 14:36, July 28, 2016. This URL is a permanent link to this version of this page.
A symmetric matrix is a square matrix that equals its transpose:
- A = AT
Thus the entries of A satisfy: <math>a_{ij} = a_{ji}</math>.
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.