In linear algebra there are two equivalent definitions of what it means for a function to be linear:

Definition 29 A function $f : {\mathbb F}_2^n \to {\mathbb F}_2$ is linear if either of the following equivalent conditions hold:

$f(x+y) = f(x) + f(y)$ for all $x, y \in {\mathbb [...]

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Ryan O'Donnell: Yes, thanks!Dmitry Sokolov: Exercise 28. Maybe $A \in \{-1, 1\}$ istead of $A \in \mathb...Ryan O'Donnell: Fixed, thanks!Ryan O'Donnell: It's the Holder conjugate of $q$ (i.e., the number satisfyin...Gautam Kamath: Is $q'$ defined here?Gautam Kamath: On this page, Hölder is displaying for me as H{ö}lder - is t...Ryan O'Donnell: Yes, you're right. This is not a well-written proof by the ...