Proposition 1

Suppose $E$ is finite-dimensional, and $A = K$ or $A = K(i)$. If $\Phi$ is a positive non-degenerate hermitian form on $E$, then the extensions of $\Phi$ to $\bigotimes^p E$ and $\wedge^p E$ ($p > 0$), as well as the inverse form of $\Phi$, are positive non-degenerate hermitian forms.

This follows at once from the existence of an orthonormal basis of $E$, and from prop. 2, $§ 6$, no 1.

Prop. 1 remains true if « positive non-degenerate » is replaced everywhere by « positive ».