- #1

- 746

- 8

**Lets define trace for each square matrix [itex]A[/itex] its trace as sum of its diagonal elements, so [itex]tr_{n}(A)=\sum_{j=1}^{n}a_{j,j}[/itex]. Now proove that trace is a linear functional for all square matrix.**

I would be happy to know what has to be true for anything to be a linear functional?

If I understand correctly, linear functional works on a vector but returns a real or complex number. So linear functional is a scalar product. Now what?