🎬how symmetric and anti-symmetric tensors behave by visualizing their effect on a sphere

The visualization uses a sphere as a reference shape. The tensor's components define a transformation matrix that warps the sphere into a new shape. You'll see that symmetric tensors create stretches and compressions along specific axes, while anti-symmetric tensors cause a rotation. This is because a general linear transformation can be decomposed into a rotation, a shear, and a stretch—the symmetric part handles the stretch and shear, and the anti-symmetric part handles the rotation.

Operations and Properties of Tensors | Condensed Notesviadean on Notion