def eigenvalue_sensitivity(T, k):
    r"""Sensitivity matrix of a specified eigenvalue.

    Parameters
    ----------
    T : (M, M) ndarray
        Transition matrix
    k : int
        Compute sensitivity matrix for k-th eigenvalue

    Returns
    -------
    S : (M, M) ndarray
        Sensitivity matrix for k-th eigenvalue.

    """
    T = _types.ensure_ndarray_or_sparse(T, ndim=2, uniform=True, kind='numeric')
    if _issparse(T):
        _showSparseConversionWarning()
        eigenvalue_sensitivity(T.todense(), k)
    else:
        return dense.sensitivity.eigenvalue_sensitivity(T, k)