Let $H_{\mathbf{Q}}$ and $H_{\mathbf{Q}}^'$ be two pure Hodge structures of weight $n$ and $n'$ respectively. How do you prove the following simple fact:

**fact:** If $n>n'$ and $f:H_{\mathbf{Q}}\rightarrow H_{\mathbf{Q}}^'$ is a morphism which respects the filtrations over $\mathbf{C}$, then $f=0$.

I don't quite see how to use the assumption $n>n'$...

**added**

My original question was related to the fact that asking the morphism to be compatible with the torus action seems to be a stronger condition that only asking for the filtration to be preserved. And I guess that in general this is all you can say. This reflexion was motivated by Deligne Scholie 5.1 in Hodge 1 which says the following:

**Scholie 5.1** Soit $H$ et $H'$ des structures de Hodge de poids $n$ et $n'$ avec $n>n'$.Soit $f:H_{Q}\rightarrow H_Q'$ un morphisme tel que $f:H_C\rightarrow H_C'$ respecte $F$. Alors $f=0$.

**Q:** So how should I interpret Scholie 5.1?