def matrix_find_eigenvalues(matrix):
eigenvalues = []
eigenvalues.append(
matrix_inverse_power_iteration(matrix, 0.0, 0.00000000000001, 20000))
eigenvalues.append(matrix_power_iteration(matrix, 0.0000000001, 20000))
find_middle_eigenvalue(matrix, eigenvalues, eigenvalues[0], eigenvalues[1])
return eigenvalues
def hilbert_matrix_power_iteration_test():
selection = [4, 6, 8, 10]
hilbert_matrix = []
solution = []
# Create the hilbert matrices and their corresponding Q factorization matrix.
for n in selection:
hilbert_matrix.append([[1 / (1 + i + j) for i in range(n)]
for j in range(n)]) # Hilbert Matrix generator
solution.append(
matrix_power_iteration(hilbert_matrix[-1], 0.000000001, 10000))
for i in range(0, len(selection)): # 4, 6, 8, 10
#print(matrix_mult(hilbert_matrix[i],convert_vec_mat(solution[i])))
print("Largest Eigen Value for " + str(selection[i]) + "x" +
str(selection[i]) + ": " + str(solution[i]))
def matrix_condition_number(matrix):
smallest_eigenvalue = matrix_inverse_power_iteration(
matrix, 0, 0.00000000000001, 20000)
largest_eigenvalue = matrix_power_iteration(matrix, 0.0000000001, 20000)
return abs(largest_eigenvalue / smallest_eigenvalue)