Merge branch 'main' of https://gitea.fhgr.ch/zimmersandro/cds-404

requirements.txt

@@ -2,4 +2,5 @@ numpy==2.4.3
 matplotlib==3.10.8
 ipykernel==7.2.0
 scipy==1.17.1
-black==26.3.1
+black==26.3.1
+sympy==1.14.0

src/klausurvorbereitung/matrix_multiplikation.py

@@ -0,0 +1,12 @@
+import numpy as np
+P = [[0, 0, 1], [0, 1, 0], [1, 0, 0]]
+L = [[1, 0, 0], [1, 1, 0], [1, 1, 1]]
+R = [[3, 1, 1], [0, 3, 1], [0, 0, 0]]
+PL = np.dot(P, L)
+A = np.dot(PL, R)
+print(A.trace())
+
+Q = [[0, -1], [1, 0]]
+R = [[1, 2], [0, 3]]
+A = np.dot(Q, R)
+print(A.trace())

src/klausurvorbereitung/spec_a.py

@@ -0,0 +1,23 @@
+import numpy as np
+import sympy as sp
+
+Q = [[0, 1, 0], [1, 0, 0], [0, 0, 1]]   # Q Matrix
+R = [[3, 1, 1], [0, 3, 1], [0, 0, 3]]   # R Matrix
+
+A = np.dot(Q, R)    # Matrix multiplikation
+
+print(np.linalg.det(A)) # Determinante
+
+AT = np.transpose(A)  # A transponiert
+AI = np.linalg.inv(A) # A Inverse
+print(AT == AI) # Orthogonal wenn True
+
+print(A.trace())    # Spur von A
+
+# Eigenwerte berechnen
+M = sp.Matrix(A)    # Sympy Matrix erstellen
+spektrum = M.eigenvals()    # Eigenwerte berechnen
+print(list(spektrum.keys()))    # Eigenwerte anzeigen
+
+QA = np.dot(Q, A)   # QR Zerlegung Gleichung umstellen
+print(QA == R)  # True wenn's stimmt

src/klausurvorbereitung/sympy_solve.py

@@ -0,0 +1,5 @@
+import sympy as sp
+x = sp.symbols("x")
+eq = sp.Eq(x**2 - 2 * x + 3, 0)
+solution = sp.solve(eq, x)
+print(solution)