From 1773466fef0b6fd417f257c1f3806f9421abf6e2 Mon Sep 17 00:00:00 2001
From: 8oldr <8oldr@proton.me>
Date: Fri, 16 Oct 2026 16:59:36 +0300
Subject: Corrected columns of V in SVD, and singular vectors definitions

---
 lecture_1.typ | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/lecture_1.typ b/lecture_1.typ
index b46df53..756691d 100644
--- a/lecture_1.typ
+++ b/lecture_1.typ
@@ -158,7 +158,7 @@ $
 $
 We denote $sigma_i = Sigma_(i,i) : 1 <= i <= k$, and call $sigma_1, dots, sigma_k$ the singular values of $M$.
 
-Let $u_1, dots, u_n$ be the columns of $U$, and $v_1, dots, v_n$ be the columns of $V$. This allows the following:
+Let $u_1, dots, u_n$ be the columns of $U$, and $v_1, dots, v_m$ be the columns of $V$. This allows the following:
 $
   M dot v_i & = U dot Sigma dot overbrace(V^T dot v_i, e_i) \
             & = U dot Sigma dot e_i \
@@ -174,7 +174,7 @@ $
   M^T = (U Sigma V^T)^T = V Sigma^T U^T
 $
 
-*Definition*: $U = u_1, dots, u_n, V = v_1, dots, v_n$ are called the _singular vectors_ of $M$.
+*Definition*: $U = u_1, dots, u_n, V = v_1, dots, v_m$ are called the _singular vectors_ of $M$.
 
 *Definition* (operator norm): $M in M_(n times m) (RR), quad norm(M)_"op" = max{norm(M dot v) : v in RR^m and norm(v) =
   1}$ (may be considered the maximum increase that $M$ can do to a vector).
-- 
cgit