Given a basis A = {a1,a2...an} we can always translate coordinates originally expressed with this basis to another basis A' = {a1',a2'...an'}. To do this we simply do some matrix-multiplication and it turns out that the change of basis matrix equals a square matrix whose rows are the coordinates of the original basis vectors written in terms of the new basis-vectors. I'm finding this a little hard to understand intuitively - can someone give me an example from maybe R^2 that shows why this is in an intuitive manner.(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!

# Change of basis matrix

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