| # Eigenvalue Decomposition of a Symmetric Matrix Symmetric Matrices > Definitions > Example Let We solve for the characteristic equation: Hence the eigenvalues are , . For each eigenvalue , we look for a unit-norm vector such that . For , we obtain the equation in which leads to (after normalization) to an eigenvector . Similarly for we obtain the eigenvector . Hence, admits the SED See also: Sums-of-squares for a quadratic form.