Hello,
I am having questions with tensors. I know that not all matrices are tensor. Tensor is a homogeneous, linear and vector valued function. So my questions are:
- Are all 3*3 matrices tensors?
- Are all anisymmetric second order tensors orthogonal?
Thanks.
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1. No. Any 3x3 matrix could be a matrix of the components of a second order tensor with a given basis. The thing tha makes the ensemble a tensor is how that matrix of numbers transforms when the basis vectors are changed.
2. To each other? No. Consider multiplying a given antisymmetric tensor by a constant. It is not orthogonal to the original antisymmetric tensor.
To all symmetric second order tensors, yes.
Matt Lewis
Los Alamos, New Mexico