Normally, if you have an orthonormal basis for a space, you can just apply your metric tensor to get your dual basis, since for an orthonormal basis all the dot products between the base vectors will boil down to a Kronecker delta. However, in Minkowski space, the dot product between a unit vector and itself may also be -1, rather than just 1, so a base vector like this does not meet the requirements if you're constructing your dual basis. Does that mean that simply applying your metric tensor need not produce your dual basis? Or does the definition of the dual basis change to allow the -1?(adsbygoogle = window.adsbygoogle || []).push({});

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Dual basis in Minkowski space

**Physics Forums | Science Articles, Homework Help, Discussion**