Let $f:V\to W$ be a surjective homomorphism of finite-dimensional vector spaces over $k$. Let $\|\raisebox{1.72218pt}{.}\|_{V}$ and $\|\raisebox{1.72218pt}{.}\|_{W}$ be norms of $V$ and $W$, respectively. We assume that $\dim_{k}W=1$ and $\|\raisebox{1.72218pt}{.}\|_{W}$ is the quotient norm of $\|\raisebox{1.72218pt}{.}\|_{V}$ in terms of the surjection $f:V\to W$. We set $V_{k^{\prime}}:=V\otimes_{k}k^{\prime}$ and $W_{k^{\prime}}:=W\otimes_{k}k^{\prime}$. Let $\|\raisebox{1.72218pt}{.}\|_{V,k^{\prime}}$ and $\|\raisebox{1.72218pt}{.}\|_{W,k^{\prime}}$ be the norms of $V_{k^{\prime}}$ and $W_{k^{\prime}}$ obtained by the scalar extensions of $\|\raisebox{1.72218pt}{.}\|_{V}$ and $\|\raisebox{1.72218pt}{.}\|_{W}$, respectively. Then $\|\raisebox{1.72218pt}{.}\|_{W,k^{\prime}}$ is the quotient norm of $\|\raisebox{1.72218pt}{.}\|_{V,k^{\prime}}$ in terms of the surjection $f_{k^{\prime}}:=f\otimes\mathrm{id}_{k^{\prime}}:V_{k^{\prime}}\to W_{k^{\prime}}$.