numpy.linalg.eigvalsh¶

numpy.linalg.eigvalsh(a, UPLO='L')

Compute the eigenvalues of a Hermitean or real symmetric matrix.

Parameters: a : array_like, shape (M, M) A complex or real matrix whose eigenvalues and eigenvectors will be computed. UPLO : {‘L’, ‘U’}, optional Specifies whether the calculation is done with data from the lower triangular part of a (‘L’, default) or the upper triangular part (‘U’). w : ndarray, shape (M,) The eigenvalues, each repeated according to its multiplicity. They are not necessarily ordered. LinAlgError : If the eigenvalue computation does not converge.

eigh
eigenvalues and eigenvectors of symmetric/Hermitean arrays.
eigvals
eigenvalues of general real or complex arrays.
eig
eigenvalues and eigenvectors of general real or complex arrays.

Notes

This is a simple interface to the LAPACK routines dsyevd and zheevd that sets the flags to return only the eigenvalues of real symmetric and complex Hermetian arrays respectively.

The number w is an eigenvalue of a if there exists a vector v satisfying the equation dot(a,v) = w*v. Alternately, if w is a root of the characteristic equation det(a - w[i]*I) = 0, where det is the determinant and I is the identity matrix.

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