If we're working in R^n and we consider the elements of a basis for R^n to be the column vectors of an nxn invertible matrix B, then what is the relationship between B and the matrix whose row vectors represent elements of the corresponding dual basis for R^n*? My guess, which Wikipedia helped me formulate, is that the row vectors of the inverse of B constitute the dual basis, but I'm still not sure. Also, if we're working in general finite-dimensional vector spaces, does the process of finding a dual basis become harder, or is it trivial once you know how to do it for R^n?(adsbygoogle = window.adsbygoogle || []).push({});

Thanks.

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

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!

# Relationship of Basis to Dual Basis

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