From 68b599eea48b9010c6f67524f34b96c08e02939c Mon Sep 17 00:00:00 2001
From: alexander <alexander@ideapad>
Date: Mon, 2 Feb 2026 12:40:23 +0100
Subject: [PATCH] Fixed complex

---
 src/cheatsheets/LinearAlgebra.typ | 18 +++++++++++++++++-
 src/lib/mathExpressions.typ       |  5 ++---
 2 files changed, 19 insertions(+), 4 deletions(-)

diff --git a/src/cheatsheets/LinearAlgebra.typ b/src/cheatsheets/LinearAlgebra.typ
index edf95a1..c98942c 100644
--- a/src/cheatsheets/LinearAlgebra.typ
+++ b/src/cheatsheets/LinearAlgebra.typ
@@ -262,7 +262,7 @@
                 $ip(O v, O w) = ip(v, w)$
             ],
             [*Unitair*], [
-
+                $V^* )$
             ],
             [*Diagonaliserbar*], [
                 $exists A = B D B^(-1)$, $D$ diagonal,
@@ -398,6 +398,22 @@
 
     #bgBlock(fill: colorMatrix)[
         #subHeading(fill: colorMatrix)[Matrix Normen]
+
+        $|| dot ||_M$ Matrix Norm, $|| dot ||_V$ Vektornorm
+
+        Generisch Vektor Norm: $|| v ||_p = root(p, sum_(k=1)^n (x_k)^p)$
+
+        - submultiplikativ: $||A B||_"M" <= ||A||||B||$
+        - verträglich mit einer Vektornorm: $||A v||_"V" <= ||A||_"M" ||v||_"V"$
+
+        *Frobenius-Norm* $||A||_"M" = sqrt(sum_(i=1)^m sum_(j=1)^n a_(m n)^2)$
+
+        *Induzierte Norm* $||A||_"M" = sup_(v in V without {0}) (||A v||_V)/(||v||_V)$\
+        $ = sup_(||v|| = 1) (||A v||_V)/(||v||_V)$
+            - submultiplikativ
+            - verträglich mit einer Vektornorm $||dot||_V$
+
+        *maximale Spaltensumme* $||A||_r = max_(1<= i <= n) sum_(j=1)^n |a_(j)|$
     ]
 
     #bgBlock(fill: colorMatrix)[
diff --git a/src/lib/mathExpressions.typ b/src/lib/mathExpressions.typ
index 848f623..5930fd7 100644
--- a/src/lib/mathExpressions.typ
+++ b/src/lib/mathExpressions.typ
@@ -6,9 +6,8 @@
 #let Bild(x) = $op("Bild")(#x)$
 #let Rang(x) = $op("Rang")(#x)$
 #let Eig(x) = $op("Eig")(#x)$
-
+#let lim = $limits("lim")$
 #let ip(x, y) = $lr(angle.l #x, #y angle.r)$
 
 #show math.integral: it => math.limits(math.integral)
-#show math.sum: it => math.limits(math.sum)
-#let lim = $limits("lim")$
\ No newline at end of file
+#show math.sum: it => math.limits(math.sum)
\ No newline at end of file