let V be the vector space of m x n matrices over R. prove that :
phi(A,B) = trace((transpose(B))*A)
defines an inner product in V.
cant work out where to start here. any pointers in the right direction would be appreciated.
thanks
let V be the vector space of m x n matrices over R. prove that :
phi(A,B) = trace((transpose(B))*A)
defines an inner product in V.
cant work out where to start here. any pointers in the right direction would be appreciated.
thanks
This problem is just an exercise in notation usage. Without TeX it is next to impossible to display. However, here is a bit of guidance.
This idea is to show that this inner product is equivalent to the usual inner product defined on the space nxn matrices. I will give a good reference Linear Algebra by Larry Smith. He shows how to work this out for <A,B>=tr{AB^T}. But his work is easily modified to this problem.