new methods; eigenvalue. condition number implemetation

eigenvalue module, readme and demo update. condition number implemented in linalg.py

examples/demo.py

@@ -1,6 +1,6 @@
 import sys
 
-sys.path.append("../")
+# sys.path.append("../")
 from numethods import *
 
 
@@ -41,6 +41,9 @@ def demo_qr():
 
 
 def demo_roots():
+    f = lambda x: x**2 - 2
+    df = lambda x: 2 * x
+
     # Newton
     steps = NewtonRoot(f, df, x0=1.0).trace()
     print("Newton Method Trace (x^2 - 2):")
@@ -85,9 +88,37 @@ def demo_differentiation():
     print("Second derivative:", SecondDerivative(f, x0))
 
 
+def demo_eigen():
+    # Not sure about eigenvalue methods but let's include some demos
+
+    A = Matrix([[4, 1, 1], [1, 3, 0], [1, 0, 2]])
+    print("\n=== Power Iteration ===")
+    solver_pi = PowerIteration(A, tol=1e-12, max_iter=100)
+    lam, x = solver_pi.solve()
+    solver_pi.trace()
+    print(f"Dominant eigenvalue ≈ {lam:.6f}, eigenvector ≈ {x}\n")
+
+    print("\n=== Inverse Power Iteration (shift=0) ===")
+    solver_ip = InversePowerIteration(A, shift=0.0, tol=1e-12, max_iter=100)
+    mu, x = solver_ip.solve()
+    solver_ip.trace()
+    print(f"Smallest eigenvalue ≈ {mu:.6f}, eigenvector ≈ {x}\n")
+
+    print("\n=== Rayleigh Quotient Iteration ===")
+    solver_rqi = RayleighQuotientIteration(A, tol=1e-12, max_iter=20)
+    mu, x = solver_rqi.solve()
+    solver_rqi.trace()
+    print(f"Eigenvalue ≈ {mu:.6f}, eigenvector ≈ {x}\n")
+
+    M = Matrix([[3, 1, 1], [-1, 3, 1], [1, 1, 3], [0, 2, 1]])
+    U, S, V = SVD(M).solve()
+    print("Singular values:", S)
+
+
 if __name__ == "__main__":
     demo_linear_solvers()
     demo_roots()
     demo_interpolation()
     demo_qr()
     demo_differentiation()
+    demo_eigen()