Bilinear forms are examples of these objects which also include bivectors and linear transformations.
The manipulation of these objects in order to produce certain expressions is known as index gymnastics. Riemann and Christo el name one of these objects used to express the curvature of manifolds. Contraction is an operation reducing the total order of these objects by two, and the most commonly used notation for these objects is Ricci calculus. Bilinear forms are examples of these objects which also include bivectors and linear transformations. One of these objects named for Cauchy is used to describe the stress of a material, and these objects describe linear relations like the inner product and cross product. For ten points, identify these objects which generalize vectors and matrices. 
The manipulation of these objects in order to produce certain expressions is known as index gymnastics.
tensors