From 8914ab49077fd89b54e26f674fbbdaaea82cbed1 Mon Sep 17 00:00:00 2001
From: Samsons Rostovs <samsons.rostovs@gmail.com>
Date: Sun, 3 Aug 2025 17:41:21 +0200
Subject: [PATCH 1/2] LU decomposition typo & suggestion

U and L switched, and suggested more details to the decomposition process
---
 semester1/linalg/linalg.typ | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/semester1/linalg/linalg.typ b/semester1/linalg/linalg.typ
index 14ecddc..da57690 100644
--- a/semester1/linalg/linalg.typ
+++ b/semester1/linalg/linalg.typ
@@ -175,7 +175,7 @@ Basically $A x = b$.
 
 == LU Decomposition
 
-Run REF on $A in RR^(m times n)$ to generate $L in RR^(m times n)$ and track coefficients in $U in RR^(n times n)$.
+Run REF on $A in RR^(m times n)$ to generate $U in RR^(m times n)$ and track coefficients in $L in RR^(n times n)$, where $L$ contains $1$'s on the diagonal and the opposite values of the operations performed on the corresponding rows.
 
 == Permutation Matrices
 
@@ -518,4 +518,4 @@ Any matrix $A$ can be factored as $A = U Sigma V^T$.
 - $A^T A = U Lambda_1 U^T$. Here we have that $Lambda_1 = Sigma^T Sigma$. $Sigma = "diag"(sigma_1, ..., sigma_k) "s.t." k = min(n,m)$
 - $A A^T = V Lambda_2 V^T$. Here we have that $Lambda_2 = Sigma Sigma^T$. $Sigma = "diag"(sigma_1, ..., sigma_k) "s.t." k = min(n,m)$
 - $sigma_i = sqrt(lambda_i)$.
-- For both: $Sigma$ is constructed s.t. $sigma_1 >= ... >= sigma_k >= 0$. Rank: number of non-zero singular values.
\ No newline at end of file
+- For both: $Sigma$ is constructed s.t. $sigma_1 >= ... >= sigma_k >= 0$. Rank: number of non-zero singular values.

From c1ea774d3f033a57307cb1baa083ebd4d87ffdd9 Mon Sep 17 00:00:00 2001
From: Shivram Sambhus <shivram.sambhus@gmail.com>
Date: Mon, 4 Aug 2025 16:04:50 +0200
Subject: [PATCH 2/2] build pdf

---
 semester1/linalg/linalg.pdf | Bin 176060 -> 181366 bytes
 1 file changed, 0 insertions(+), 0 deletions(-)

diff --git a/semester1/linalg/linalg.pdf b/semester1/linalg/linalg.pdf
index c523698393425e361803543ba757e6b2c303ef2b..12fb0f96fffc4b6bf4abddcfed7d472115afab3e 100644
GIT binary patch
