Added CT good to know sheet

src/cheatsheets/CT.typ

@@ -0,0 +1,47 @@
+#import "../lib/styles.typ" : *
+#import "../lib/common_rewrite.typ" : *
+
+#set page(
+  paper: "a4", 
+  margin: (
+    bottom: 10mm,
+    top: 5mm,
+    left: 5mm,
+    right: 5mm
+  ),
+  flipped:true,
+  numbering: "— 1 —",
+  number-align: center
+)
+
+#set text(size: 8pt)
+
+#place(top+center, scope: "parent", float: true, heading(
+  [LComputer Technik/Programmierpraktikum EI]
+))
+
+#let Allgemein = color.hsl(105.13deg, 92.13%, 75.1%)
+#let colorProgramming = color.hsl(330.19deg, 100%, 68.43%)
+#let colorNumberSystems = color.hsl(202.05deg, 92.13%, 75.1%)
+// #let colorVR = color.hsl(280deg, 92.13%, 75.1%)
+// #let colorAbbildungen = color.hsl(356.92deg, 92.13%, 75.1%)
+// #let colorGruppen = color.hsl(34.87deg, 92.13%, 75.1%)
+
+
+#let SeperatorLine = line(length: 100%, stroke: (paint: black, thickness: 0.3mm))
+#let MathAlignLeft(e) = {
+  align(left, block(e))
+}
+#columns(4, gutter: 2mm)[
+  #bgBlock(fill: colorNumberSystems)[
+    #subHeading(fill: colorNumberSystems)[ASCII Ranges]
+
+    #table(
+      columns: (1fr, 1fr, 1fr),
+      [Range], [Hex], [Bits],
+      [Lower Case], [$"0x41"..."0x5A"$], [$"XX0X XXXX"$ (bit 6)],
+      [Upper Case], [$"0x61"..."0x7A"$], [$"XX1X XXXX"$ (bit 6)],
+      [Ganz ASCII], [$"0x00"..."0x7F"$], [$"0XXX XXXX"$]
+    )
+  ]
+]

src/cheatsheets/LinearAlgebra.typ

@@ -332,32 +332,33 @@
         #subHeading(fill: colorMatrixVerfahren)[Diagonalisierung]
         $A = R D R^(-1)$
 
-        #grid(
-            columns: (1fr, 1fr),
-            $D = mat(
-                lambda_1, 0, 0,...;
-                0, lambda_1, 0, ...;
-                0, 0, lambda_2, ...;
-                dots.v, dots.v, dots.v, dots.down
-            )$,
-
-            $D^n = mat(
-                lambda_1^n, 0, 0,...;
-                0, lambda_1^n, 0, ...;
-                0, 0, lambda_2^n, ...;
-                dots.v, dots.v, dots.v, dots.down
-            )$
-        ) \
-
         *Rezept Diagonalisierung*
 
-        1. *EW* bestimmen
-        2. $chi_A$ bestimmen und in $(lambda_0 - lambda)^(n_0) dot (lambda_1 - lambda)^(n_1) ...$ Form bringen \
-            $chi_A$ nicht vollstandig zerfällt (in $RR$), $=>$ NICHT diagonalisierbar
-        3. *EV* bestimmen
-        4. $R = mat( bar, bar, ..; v_(lambda 0), v_(lambda 1), ...; bar, bar, ...)$
-        5. $R^(-1)$ bestimmen 
-    ]
+        1. EW bestimmen: $det(A - lambda I) = 0$  \
+            $=> chi_A = (lambda_1 - lambda)^(m 1) (lambda_2 - lambda)^(m 2) ...$ 
+        2. EV bestimmen: $spann(kern(A - lambda_i I))$: $r_0, r_1, ...$
+        3. \
+            #grid(columns: (1fr, 1fr),
+            [
+                Diagnoalmatrix: $D$
+                $mat(
+                        lambda_1, 0, 0,...;
+                        0, lambda_1, 0, ...;
+                        0, 0, lambda_2, ...;
+                        dots.v, dots.v, dots.v, dots.down
+                    )
+                $
+            ],
+            [
+                Basiswechselmatrix: $R$
+                $mat(
+                    |, | , ..., |;
+                    r_0, r_1, ..., r_n;
+                    |, |, ..., |
+                )$
+            ]
+        )
+     ]
 
 
     #bgBlock(fill: colorMatrixVerfahren)[
@@ -368,31 +369,24 @@
     #bgBlock(fill: colorMatrixVerfahren)[
         #subHeading(fill: colorMatrixVerfahren)[SVD]
 
-        $A in RR^(m times n)$ zerlegbar in $A = U Sigma V^T$ \
+        $A in RR^(m times n)$ zerlegbar in $A = L S R^T$ \
 
 
-        $U in RR^(m times m)$ Orthogonal \
-        $Sigma in RR^(m times n)$ Diagonal \
-        $V in RR^(n times n)$ Orthogonal
+        $L in RR^(m times m)$ Orthogonal \
+        $S in RR^(m times n)$ Diagonal \
+        $R in RR^(n times n)$ Orthogonal
 
 
-        1. $A^T A$ berechnen $A^T A in RR^(k times k), k = min(n, m)$
+        1. $A A^T$ berechnen $A A^T in RR^(m times m)$
 
-        2. Eigenwerte bestimmen $det(A^T A - E lambda) = 0$ \
-            $lambda_0, lambda_1 ... lambda_k$ nach Größe sortieren \
-            Singulärewerte: $sigma_i = sqrt(lambda_i)$
+        2. $A A^T$ diagonalisieren in $R$, $D$
 
-        3. Eigenvekoren von $A^T A$ bestimmen und *Normalisieren*
-            $v_(lambda 0), v_(lambda 1), ... v_(lambda k)$ 
-
-        4. $V = mat( |, |, ..., |; v_0, v_1, ..., v_n; |, |, ..., |) --> V^T$ \
+        3. Singulärwere berechen: $sigma_i = sqrt(lambda_i) $
+        
+        4. $l_i = 1/sigma_i A v_(lambda i) quad quad L = mat( |, |, ..., |; l_0, l_1, ..., l_m; |, |, ..., |)$ \
             (Evt. zu ONB ergenze mit Gram-Schmit/Kreuzprodukt)
 
-        5. $u_i = 1/sigma_i A v_(lambda i) quad quad L = mat( |, |, ..., |; u_0, u_1, ..., u_m; |, |, ..., |)$ \
-            (Evt. zu ONB ergenze mit Gram-Schmit/Kreuzprodukt)
-
-        6. $S in RR^(n times m)$ (wie $A$):
-
+        5. $S in RR^(n times m)$ (wie $A$): \
             $S = mat(sigma_0, 0; 0, sigma_1; dots.v, dots.v; 0, 0) quad quad quad S = mat(sigma_0, 0, dots, 0; 0, sigma_1, ..., 0)$
     ]