Wolfram Alpha:

```Stress-Energy Tensor
--------------------

Tensors are geometric objects that describe linear
relations between vectors, scalars, and other tensors.
They are the counterparts of 4-vectors in Special
Relativity.

Consider the stress, σ, inside a material.  How can
we describe the forces, F, inside of it.  Imagine a
cubic region with faces of area, A, within the material.

The corresponding stress tensor is:

-         -
| σxx σxy σxz |
σ = | σyx σyy σyz |
| σzx σzy σzz |
-         -

Stress is a vector defined as F/A.  In geometry we
can represent an area as a vector.  The vector is
perpendicular to the area and the length of the vector
is proportional to the area. The forces can be written
as the dot product of the stress and the area vector.
Thus:

Fx = x component from x face + x comp. from y face
+ x comp. from z face

= σxx.Ax + σyx.Ay + σzx.Az

Fy = ....

Fz = ....

Total force: F = Fx + Fy + Fz

The off diagonal components represent shear stresses.

Tensors are defined in terms of ranks as follows.

Rank-0 tensor = scalar - no indeces
Rank-1 tensor = vector = 1d matrix - 1 index
Rank-2 tensor = 2d matrix - 2 indeces
Rank-3 tensor = 3d matrix (cube) - 3 indeces

Rank 2 Tensor
-------------

Simplest way to visualize is in terms of the OUTER
(Dyadic) product of 2 vectors A,B.

Tmn = AmBn

-             -
| A1B1 A1B2 A1B3 |
= | A2B1 A2B2 A2B3 |
| A3B1 A3B2 A3B3 |
-             -
```