# scipy.linalg.eigvalsh¶

scipy.linalg.eigvalsh(a, b=None, lower=True, overwrite_a=False, overwrite_b=False, turbo=True, eigvals=None, type=1, check_finite=True)[source]

Solve an ordinary or generalized eigenvalue problem for a complex Hermitian or real symmetric matrix.

Find eigenvalues w of matrix a, where b is positive definite:

              a v[:,i] = w[i] b v[:,i]
v[i,:].conj() a v[:,i] = w[i]
v[i,:].conj() b v[:,i] = 1

Parameters: a : (M, M) array_like A complex Hermitian or real symmetric matrix whose eigenvalues and eigenvectors will be computed. b : (M, M) array_like, optional A complex Hermitian or real symmetric definite positive matrix in. If omitted, identity matrix is assumed. lower : bool, optional Whether the pertinent array data is taken from the lower or upper triangle of a. (Default: lower) turbo : bool, optional Use divide and conquer algorithm (faster but expensive in memory, only for generalized eigenvalue problem and if eigvals=None) eigvals : tuple (lo, hi), optional Indexes of the smallest and largest (in ascending order) eigenvalues and corresponding eigenvectors to be returned: 0 <= lo < hi <= M-1. If omitted, all eigenvalues and eigenvectors are returned. type : integer, optional Specifies the problem type to be solved: type = 1: a v[:,i] = w[i] b v[:,i] type = 2: a b v[:,i] = w[i] v[:,i] type = 3: b a v[:,i] = w[i] v[:,i] overwrite_a : bool, optional Whether to overwrite data in a (may improve performance) overwrite_b : bool, optional Whether to overwrite data in b (may improve performance) check_finite : boolean, optional Whether to check that the input matrices contain only finite numbers. Disabling may give a performance gain, but may result in problems (crashes, non-termination) if the inputs do contain infinities or NaNs. w : (N,) float ndarray The N (1<=N<=M) selected eigenvalues, in ascending order, each repeated according to its multiplicity. LinAlgError : If eigenvalue computation does not converge, an error occurred, or b matrix is not definite positive. Note that if input matrices are not symmetric or hermitian, no error is reported but results will be wrong.

eigvals
eigenvalues of general arrays
eigh
eigenvalues and right eigenvectors for symmetric/Hermitian arrays
eig
eigenvalues and right eigenvectors for non-symmetric arrays

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