A symmetric second-order tensor can be visualized by
defining an ellipsoid from its eigenvectors. The length of
the eigenvectors is determined by the corresponding
eigenvalues.

In above pictures a single point load is applied to an elastic material,
resulting in singular stress and strain values.
The top image visualizes the stress field with tensor
ellipsoids. In stress analysis the axes of the ellipsoids are the principle
direction of the stress. At the surface of the
material the ellipsoids flatten because there is no stress
perpendicular to the surface. Near the singularity
the ellipsoids elongate and point in the direction of the load point.

The bottom picture shows the same tensor field visualized with
hyperstreamlines. Note how the hypersteamlines point in
direction of the point load and flare as they approach
the stress singularity.
Hyperstreamlines are explained in
image 1