- #1
christodouloum
- 35
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1. While reading notes on group theory there is a step I could not reproduce although it seems to me it should be straightforward. Probably there is something I am missing on tensor indices notation. Since R is an orthogonal matrix you can...
2 ...go from \epsilon _{lmn}R_{il}R_{jm}R_{kn}=\epsilon_{ijk}
to \epsilon_{lmn}R_{jm}R_{kn}=\epsilon_{ijk}R_{il}
3. Since R is orthogonal I wrote down R_{il}R_{ir}=\delta _{lr}. So I multiply both sides by R_il and by relabelling r with l it works. But can I do that?
2 ...go from \epsilon _{lmn}R_{il}R_{jm}R_{kn}=\epsilon_{ijk}
to \epsilon_{lmn}R_{jm}R_{kn}=\epsilon_{ijk}R_{il}
3. Since R is orthogonal I wrote down R_{il}R_{ir}=\delta _{lr}. So I multiply both sides by R_il and by relabelling r with l it works. But can I do that?
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