Symmetric matrix

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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.