Let F:M(nxn)R->R where F(A) = tr(A).
The dimention of
Since the trace of a matrix is the sum of the diagonal any non diagonal entry is mapped to 0. Since there are n entries on the diagonal that means that there are
non diagonal entries.
The trace of the matrix is
So this equation has n-1 free parameters in it.
So the dimention of the kernal is
.
What do you think about the image?