From ad316fe1071fc48a92720c578ba6a97b0ab1e46d Mon Sep 17 00:00:00 2001 From: David Wong Date: Fri, 19 Sep 2025 12:00:08 -0400 Subject: [PATCH] fix ipa explanation --- book/src/plonk/inner_product.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/book/src/plonk/inner_product.md b/book/src/plonk/inner_product.md index f2591f025bf..49c44ef2446 100644 --- a/book/src/plonk/inner_product.md +++ b/book/src/plonk/inner_product.md @@ -173,7 +173,7 @@ So the new inner product should be: $$ \begin{align} -\vec{z'} =& \langle \vec{a'}, \vec{b'} \rangle \\ +z' =& \langle \vec{a'}, \vec{b'} \rangle \\ =& \langle \begin{pmatrix}x^{-1} a_1 + x a_3 \\ x^{-1} a_2 + x a_4 \end{pmatrix}, \begin{pmatrix}x b_1 + x^{-1} b_3 \\ x b_2 + x^{-1} b_4 \end{pmatrix} \rangle \\ =& (a_1b_1 + a_2b_2 + a_3b_3 + a_4b_4) + x^{-2} (a_1b_3 + a_2b_4) + x^2 (a_3b_1 + a_4b_2) \\ =& z + x^{-2} (L_z) + x^2 (R_z)