From 1f4edfb7374e6dee9a3331397d59900b78226002 Mon Sep 17 00:00:00 2001 From: Matej Briskar Date: Sat, 12 Oct 2019 17:04:05 -0700 Subject: [PATCH] Apply proper sqrt on both sides in the proof of Perceptron Convergence Theorem. --- book/perc.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/book/perc.tex b/book/perc.tex index 0f85682..e262463 100644 --- a/book/perc.tex +++ b/book/perc.tex @@ -586,7 +586,7 @@ \section{Perceptron Convergence and Linear Separability} Now we put together the two things we have learned before. By our first conclusion, we know $\dotp{\vw^*}{\vw\kth} \geq k \ga$. But - our second conclusion, $\sqrt{k} \geq \norm{\vw\kth}^2$. Finally, + our second conclusion, $\sqrt{k} \geq \norm{\vw\kth}$. Finally, because $\vw^*$ is a unit vector, we know that $\norm{\vw\kth} \geq \dotp{\vw^*}{\vw\kth}$. Putting this together, we have: \begin{equation}