Thus a metric tensor is a covariant symmetric tensor. This table shows important examples of tensors on vector spaces and tensor fields on manifolds. There are several operations on tensors that again produce a tensor. The covariance matrix is related to the moment of inertia tensor for multivariate distributions. The strain tensor is a symmetric tensor. Formula for harmonical invariant tensor was found in paper. The fundamental object is called the Riemann curvature tensor. Directional derivatives are often used in introductory derivations of the Riemann curvature tensor. These symmetries are called the minor symmetries of the stiffness tensor c. Here formula 3 is the inverse matrix to the metric tensor formula 4. For the same equations expressed using tensor calculus or differential forms, see alternative formulations. The ellipsoid formalism functions also as a mathematical method of organizing tensor data. Let formula 86 be an antisymmetric tensor of rank "r". These are called the major symmetries of the stiffness tensor. Similarly, the symmetry of the infinitesimal strain tensor implies that .