From 41a84d6996b3e5ac70183bbb12dfb3e741803bc0 Mon Sep 17 00:00:00 2001
From: zimmersandro <sandro.zimmermann@stud.fhgr.ch>
Date: Wed, 22 Apr 2026 20:34:07 +0200
Subject: [PATCH] feat: task 7 Matrix Spur und Determinante mit numpy und sympy
 berechnen

---
 src/lineare_algebra/task7.py | 114 +++++++++++++++++++++++++++++++++++
 1 file changed, 114 insertions(+)
 create mode 100644 src/lineare_algebra/task7.py

diff --git a/src/lineare_algebra/task7.py b/src/lineare_algebra/task7.py
new file mode 100644
index 0000000..64608bc
--- /dev/null
+++ b/src/lineare_algebra/task7.py
@@ -0,0 +1,114 @@
+# %%
+# Import
+import numpy as np
+
+# Parameter
+matrizen = [
+    np.array([[2, 3], [4, 5]]),
+    np.array([[2, 3], [4, 6]]),
+    np.array([[-1, 3, 0], [0, 2, 0], [1, 2, -1]]),
+    np.array([[-2, 4, 8], [1, -2, -4], [6, -3, 12]]),
+    np.array([[1, 0, 3, 0], [4, -2, 12, 6], [1, 2, 3, -4], [3, 3, 15, -2]]),
+    np.array(
+        [
+            [1, np.sqrt(3), 8, -np.sqrt(2)],
+            [-13, 3, np.sqrt(2), 0],
+            [np.sqrt(17), -1, 0, 0],
+            [2, 0, 0, 0],
+        ]
+    ),
+    np.array(
+        [
+            [2, -3, 5, 1, 4],
+            [2, -3, 1, -6, 18],
+            [4, -3, 9, 6, 10],
+            [-2, 4, -6, -1, -1],
+            [-6, 11, -23, -14, 9],
+        ]
+    ),
+    np.array(
+        [
+            [1, 0, 0, 1, 0],
+            [1, 0, 0, -1, 0],
+            [0, 1, 1, 0, 0],
+            [0, -1, 1, 0, 0],
+            [0, 0, 0, 0, np.sqrt(2)],
+        ]
+    ),
+]
+
+# Layout
+print(60 * "-")
+print("Aufgabe 3. Spur und Determinante berechnen (numpy)")
+print(__file__)
+print(60 * "-")
+
+for matrix in matrizen:
+
+    # Berechnung
+    tr = np.trace(matrix)
+    det = np.linalg.det(matrix)
+
+    # Ausgabe
+    print(f"\n{matrix}\n")
+    print(f"Spur: {tr:.3f}")
+    print(f"Determinante: {det:.3f}")
+    print(60 * "-")
+
+# %%
+# Import
+import sympy as sp
+from IPython.display import display, Math
+
+# Parameter
+matrizen = [
+    sp.Matrix([[2, 3], [4, 5]]),
+    sp.Matrix([[2, 3], [4, 6]]),
+    sp.Matrix([[-1, 3, 0], [0, 2, 0], [1, 2, -1]]),
+    sp.Matrix([[-2, 4, 8], [1, -2, -4], [6, -3, 12]]),
+    sp.Matrix([[1, 0, 3, 0], [4, -2, 12, 6], [1, 2, 3, -4], [3, 3, 15, -2]]),
+    sp.Matrix(
+        [
+            [1, sp.sqrt(3), 8, -sp.sqrt(2)],
+            [-13, 3, sp.sqrt(2), 0],
+            [sp.sqrt(17), -1, 0, 0],
+            [2, 0, 0, 0],
+        ]
+    ),
+    sp.Matrix(
+        [
+            [2, -3, 5, 1, 4],
+            [2, -3, 1, -6, 18],
+            [4, -3, 9, 6, 10],
+            [-2, 4, -6, -1, -1],
+            [-6, 11, -23, -14, 9],
+        ]
+    ),
+    sp.Matrix(
+        [
+            [1, 0, 0, 1, 0],
+            [1, 0, 0, -1, 0],
+            [0, 1, 1, 0, 0],
+            [0, -1, 1, 0, 0],
+            [0, 0, 0, 0, sp.sqrt(2)],
+        ]
+    ),
+]
+
+# Layout
+print(60 * "-")
+print("Aufgabe 3. Spur und Determinante berechnen (sympy)")
+print(__file__)
+print(60 * "-")
+
+for matrix in matrizen:
+
+    # Berechnung
+    tr = sp.trace(matrix)
+    det = sp.det(matrix)
+
+    # Ausgabe
+    display(Math(rf"{sp.latex(matrix)}"))
+    display(Math(rf"\text{{Spur: }}{sp.latex(tr)}"))
+    display(Math(rf"\text{{Determinante: }}{sp.latex(det)}"))
+    print(60 * "-")