Mathematics Asked by Ivan Bravo on December 6, 2020
I was doing an exercise and I saw this property, I would like to know why it’s true.
Let $V$ be a $mathbb{K}$-dimensional vector space and Let $f$ be a bilinear form. Given $S subseteq V$, we define: $S^perp$={$alpha in V | f(alpha, beta)=0$
$forall beta in S$}
{0}$^perp$=$V$
Answered by azif00 on December 6, 2020
Every $xin V$ satisfies that $f(x,0)=0$ for $f$ is bilinear. And given that ${0}$ is only composed by $0$ (obviously) then every $xin V$ is in the ortogonal complement of $0$.
Answered by Iesus Dave Sanz on December 6, 2020
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