Hi everyone,(adsbygoogle = window.adsbygoogle || []).push({});

Can anyone explain the following to me?

Given a basis beta for an n-dimensional vector space V over the field F, "the standard representation of V with respect to beta is the function phi_beta(x)=[x]_beta for each x in V." This is from my textbook.

It then proceeds to give the following example:

Let beta = {(1,0),(0,1)} and gamma = {(1,2),(3,4)}, where beta and gamma are ordered bases for R^2. For x=(1,-2), we have

phi_beta(x)=[x]_beta = (1,-2) and phi_gamma(x)=[x]_gamma = (-5,2).

I kind of see where the definition is going, and I understand how to find matrix representations of a transformation, but I just don't see what this standard representation thing is.

Where did the (1,-2) and the (-5,2) come from? How did they get these from the bases beta and gamma? I'm so confused! Any enlightenment would be wonderful.

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!

# Standard representation of a vector space

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