# Symmetric matrix

From Conservapedia

A **symmetric matrix** is a square matrix that equals its transpose:

*A*=*A*^{T}

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.