nvectors of real symmetric or complex Hermitian (conjugate symmetric) arrays. scipy.linalg.eigvals : Similar function in SciPy. Notes ----- .. versionadded:: 1.8.0 Broadcasting rules apply, see the `numpy.linalg` documentation for details. This is implemented using the ``_geev`` LAPACK routines which compute the eigenvalues and eigenvectors of general square arrays. Examples -------- Illustration, using the fact that the eigenvalues of a diagonal matrix are its diagonal elements, that multiplying a matrix on the left by an orthogonal matrix, `Q`, and on the right by `Q.T` (the transpose of `Q`), preserves the eigenvalues of the "middle" matrix. In other words, if `Q` is orthogonal, then ``Q * A * Q.T`` has the same eigenvalues as ``A``: >>> from numpy import linalg as LA >>> x = np.random.random() >>> Q = np.array([[np.cos(x), -np.sin(x)], [np.sin(x), np.cos(x)]]) >>> LA.norm(Q[0, :]), LA.norm(Q[1, :]), np.dot(Q[0, :],Q[1, :]) (1.0, 1.0, 0.0) Now multiply a diagonal matrix by ``Q`` on one side and by ``Q.T`` on the other: >>> D = np.diag((-1,1)) >>> LA.eigvals(D) array([-1., 1.]) >>> A = np.dot(Q, D) >>> A = np.dot(A, Q.T) >>> LA.eigvals(A) array([ 1., -1.]) # random r