feat: task3 Matrix Berechnungen

src/lineare_algebra/task3.py

@@ -0,0 +1,85 @@
+#%%
+import numpy as np
+import sympy as sp
+from IPython.display import display, Math
+
+#%%
+# Parameter
+A = np.array([[1,3,-1],[4,-2,8]])
+B = np.array([[-3,9,3],[-6,6,3]])
+
+# Layout
+print(60 * "-")
+print("Aufgabe 3. Matrizen berechnen (Numpy)")
+print(__file__)
+print(60 * "-")
+
+#Berechnung
+C=A+B
+D=-2*A
+E=(1/3)*B
+F=2*B-A
+
+#Ausgabe
+print(f"C = {C}")
+print(f"D = {D}")
+print(f"E = {E}")
+print(f"F = {F}")
+print(60 * "-")
+
+#%%
+# Parameters
+A = sp.Matrix([[1, 3, -1], [4, -2, 8]])
+B = sp.Matrix([[-3, 9, 3], [-6, 6, 3]])
+
+# Layout
+print("-" * 60)
+print("Aufgabe 3. Matrizen berechnen (Sympy)")
+print(__file__)
+print("-" * 60)
+
+# Berechnung
+C = A + B
+D = -2 * A
+E = sp.Rational(1, 3) * B   # ← keeps fractions exact, e.g. 1 not 0.333...
+F = 2 * B - A
+
+# Ausgabe – symbolic, paper-style
+for name, matrix in [("C", C), ("D", D), ("E", E), ("F", F)]:
+    display(Math(rf"{name} = {sp.latex(matrix)}"))
+
+print("-" * 60)
+
+# %%
+# Parameters
+A = sp.Matrix([[4,-3,2],[6,2,5],[-1,-2,3]])
+B = sp.Matrix([[3,4],[1,2],[5,6]])
+u = sp.Matrix([0,2,-4])
+v = sp.Matrix([1,3,-3])
+
+# Layout
+print("-" * 60)
+print("Aufgabe 6. Produkte mit Matrizen")
+print(__file__)
+print("-" * 60)
+
+# Berechnung
+berechnungen = [
+    ("a", lambda: A * B),
+    ("b", lambda: B * A),
+    ("c", lambda: A * u),
+    ("d", lambda: A ** 2),
+    ("e", lambda: B * B),
+    ("f", lambda: v.T * u),
+    ("g", lambda: v * u),
+    ("h", lambda:u * v.T),
+    ("i", lambda: B.T * v),
+    ("j", lambda: v.T * B)
+]
+
+for name, berechnung in berechnungen:
+    try:
+        result = berechnung()
+        display(Math(rf"{name} = {sp.latex(result)}"))
+    except Exception as e:
+        display(Math(rf"{name} = \text{{Fehler: }} \text{{{e}}}"))