- #1
Kara386
- 208
- 2
We've been learning about tensor products. In particular, we've been looking at index notation for the tensor products of matrices like these:
##
\left( \begin{array}{cc}
a_{11} & a_{12} \\
a_{21} & a_{22} \end{array} \right)##
And
##
\left( \begin{array}{cc}
b_{11} & b_{12} \\
b_{21} & b_{22} \end{array} \right)##
In index notation the tensor product is ##(a \bigotimes b)_{ijkl} = a_{ij}b_{kl}##. And apparently, there's an expression in terms of these indices which tells you which row and which column ##a_{ij}b_{kl}## will be on. So I tried the row number being ##ik## and the column number being ##kl## and that worked up to the third row and column, then it didn't any more. I've written out the matrix and I've been staring at it, and I cannot see what the expression for row and column number is. Does anyone know it? I'd really appreciate someone showing me, because now it's going to bother me for ages. Thanks for any help! :)
##
\left( \begin{array}{cc}
a_{11} & a_{12} \\
a_{21} & a_{22} \end{array} \right)##
And
##
\left( \begin{array}{cc}
b_{11} & b_{12} \\
b_{21} & b_{22} \end{array} \right)##
In index notation the tensor product is ##(a \bigotimes b)_{ijkl} = a_{ij}b_{kl}##. And apparently, there's an expression in terms of these indices which tells you which row and which column ##a_{ij}b_{kl}## will be on. So I tried the row number being ##ik## and the column number being ##kl## and that worked up to the third row and column, then it didn't any more. I've written out the matrix and I've been staring at it, and I cannot see what the expression for row and column number is. Does anyone know it? I'd really appreciate someone showing me, because now it's going to bother me for ages. Thanks for any help! :)
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