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Eigenvalues And Eigenvectors Of A Symmetric Matrix
 Syntax `eigsym(`x```) eigsym(```x`,`e`)` See Also symeig , eigen , svd

Description
Computes the eigenvalues of the matrix x, where x is a real, double-precision or complex conjugate symmetric matrix . ``` ```If the argument e is present the eigenvectors of x are also computed. The input value of e does not matter and its output value is a unitary matrix , with the same type and dimension as x, containing the eigenvectors. ``` ```The return value is a column vector with the same type and row dimension as x containing the eigenvalues. If r is the return value, ```      e * diag(r) = x * e ```where `diag(r)` is the diagonal matrix with r along its diagonal. ``` ```This routine computes the eigenvalues and eigenvectors directly. The routine symeig uses an SVD factorization to compute the eigenvectors.

Example
If you enter ```      x  = {[3., 1.], [1., 3.]}      e  = novalue      eigsym(x, e) ``` O-Matrix will respond ```      {       2       4       } ``` If you continue by entering ```      e * e' ``` O-Matrix will respond ```      {       [ 1 , 0 ]      [ 0 , 1 ]       } ``` (Note that the complex conjugate is not necessary because e has the same type as x and hence is a real matrix.) If you continue by entering ```      e * diag({2, 4}) - x * e ``` O-Matrix will respond ```      {       [ 0 , 0 ]      [ 0 , 0 ]      } ```