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zaLWeO`ap&czGfN6xj7ZkTVG>AdcFyT0{Du};30})Bc|zdZ8^IVVrTlk z#vMBNjyXFEpk3dk)m?8ys}1eY{P|~8lx=rchMm?pBvrTUlL^jJKMYH3bJQu(X5e4U zo>6DuchN1e(rA7tRdLb?tCbo3dN7JwfLpF62U8->@Ny(wQ27=3eIvU8VnAbOs5jY( zKapYj>aj^tV5{{I`FH;=MQhgl4;BMpuc=*IdiE?#moV<~xu;(D4zxXF3Io~}6-pMt z6_{sJnR_qyPW_ diff --git a/qforms.tex b/qforms.tex index 9e64537..85f7e14 100644 --- a/qforms.tex +++ b/qforms.tex @@ -362,7 +362,11 @@ $(3)\Rightarrow(2)$ из предложения~\ref{prop:hyperbolic_plane}, $(2)\Rightarrow(1)$: если $V$~--- пространство формы $\ph$, то изотропность $\ph\perp\la -a\ra$ на пространстве $V\perp kv_1$ означает, что для некоторых $v\in V$, $\lambda\in k$, не равных одновременно 0, -выполняется $\ph(v)-a\lambda^2=0$. Если $v=0$, то $\lambda=0$; значит, $v\neq 0$. +выполняется $\ph(v)-a\lambda^2=0$. +Если форма $\ph$ изотропна, то (как следует из двух предыдущих утверждений) +она принимает вообще все значения, и $a$ в том числе. +Если же $\ph$ не изотропна, то $\ph(v)$ не может равняться +$0$, откуда $\lambda\neq 0$. Поэтому $\ph(v/\lambda)=a\lambda^2/\lambda^2=a$, что и требовалось. \end{proof}