Finding the range of the trace

[torquerotates]

Homework Statement

Find the basis for the range of the following transformation: T(A)=tr(A)

Homework Equations

tr(A)=a(1,1)+a(2,2)+...+a(n,n) {not a multiple of but just subscripts of the entries of the diagonal elements}

The Attempt at a Solution

Since the elements can be any real number, the range R(T)= all real numbers on the number line(i.e R^1). So I guess the basis is just 1? Is this right?

 

[HallsofIvy]

Yes, that is true.