With T: R^m -->R^n be linear transformation T(x) = B*x and if psi sub I is an elementary alternating k-tensor on R^n, then T*psisub I has the form:
$ T^**\psi_I $ = sigma sub [J] cJ*psi[J] where psiJ are the elementary alternating k-tensors on R^m and
where $I = (i_1,\ldots, i_k)$ and we can let $I_\sigma = (i_{\sigma(1)},\ldots, i_{\sigma(k)})$.
I'm trying to determine the coefficients of C sub J.
My proof:
T*f(x) = f(T(x)) = f(Bx) = ABx so the matrix T*f is AB
And if f = sigma sub [I] dsubI * psisub I is an alternating k-tensor on R^n, how can T*f be expressed in terms of the elementary k-tensors on R^m?
Thanks