character of tensor product of irreducible representations

Question

Question about Serre's book "Linear representations of finite groups" page 16. Suppose $V$ with character $\chi$ has a decompostion $m_1 W_1\oplus\dots\oplus m_hW_h$ where $m_i$ are non-negative integers and $W_i$ are irreducible with character $\chi_i$, so $\chi=m_1\chi_1+\dots+m_h\chi_h$. Form $W_i\otimes W_j$ with character $\chi _i\chi_j$. Serre claims that $\chi_i\chi_j$ is a linear combination of the $\chi_i$ with non-negative integer coefficients. Why?