- #1
arpon
- 235
- 16
Suppose a second rank tensor ##T_{ij}## is given. Can we always express it as the tensor product of two vectors, i.e., ##T_{ij}=A_{i}B_{j}## ? If so, then I have a few more questions:
1. Are those two vectors ##A_i## and ##B_j## unique?
2. How to find out ##A_i## and ##B_j##
3. As ##A_i## and ##B_j## has ##3+3 = 6## components in total (say, in 3-dimension), it turns out that we need only ##6## quantities to represent the ##9## components of the tensor ##T_{ij}##. Is that correct?
1. Are those two vectors ##A_i## and ##B_j## unique?
2. How to find out ##A_i## and ##B_j##
3. As ##A_i## and ##B_j## has ##3+3 = 6## components in total (say, in 3-dimension), it turns out that we need only ##6## quantities to represent the ##9## components of the tensor ##T_{ij}##. Is that correct?