eigenvalue.py

Created on January 09, 2025

871 Bytes

def mat_mult(A, B):
    # Matrix multiplication
    result = [[sum(a * b for a, b in zip(A_row, B_col)) for B_col in zip(*B)] for A_row in A]
    return result

def mat_sub(A, B):
    # Matrix subtraction
    result = [[A[i][j] - B[i][j] for j in range(len(A[0]))] for i in range(len(A))]
    return result

def identity_matrix(n):
    # Create an identity matrix of size n
    I = [[1 if i == j else 0 for j in range(n)] for i in range(n)]
    return I

# Example matrix
A = [[4, 2],
     [1, 3]]

# For simplicity, let's assume a known eigenvalue (you can use a method to find eigenvalues)
eigenvalue = 5

# Eigenvalue matrix
Lambda = [[eigenvalue if i == j else 0 for j in range(len(A))] for i in range(len(A))]

# (A - λI)
I = identity_matrix(len(A))
A_minus_lambdaI = mat_sub(A, Lambda)

print("A - λI:")
for row in A_minus_lambdaI:
    print(row)

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eigenvalue.py