Linear Algebra: basis and matrices

[Shadowz]

Hi,

I have a question about linear transformation. So given a matrix A in the basis u (denoted as A_u). Now in another basis that I don't know, A_u becomes A_v.

How can I find v? (I know u, A_u and A_v).

Thank you very much,

 

[arkajad]

You can't in general. For instance the identity matrix has in any basis the same form:

(I_u)_{ij}=(I_v)_{ij}=\delta_{ij}.