/sci/ - Science & Math

>>15999077
Not a bad video, but I do think that it is a bit confusing to call a tensor either a matrix, like when he calls the 3x3 matrix a stress tensor. To fully represent the stress tensor, you need a basis in addition to the matrix, the matrix alone is not a tensor. Tensors themselves are independent of the chosen basis, you just need a basis to represent them in this way.

For the same reason one should be careful on what means by 'vector'. A 1xm and nx1 matrices can be called vectors, but they are not tensors either. They also require a basis to represent a rank-1 tensor.

The picrel shows two different representations of the same strain tensor (principal basis and basis with maximum shear)