Question

how to do this using python

10. Create a script to calculate the Eigen values and right Eigen vectors for a given matrix. Your script should get the dimensions of the matrix from the user first and verify that the matrix is square. If the dimensions don't represent a square matrix, your script should report an error and ask for the dimensions again. If the users doesn't give you enough values (or too many values) for the given dimensions, your script should report an error and end. If given a proper matrix, your script should print the matrix, the Eigen values for the matrix and the right Eigen vectors for the matrix. The Eigen values should be in scientific notation with 3 decimal places.

Answer 1

Code:

import numpy as np
from scipy import linalg
dim = []
while(True):#run indefinitely
dim = [int(x) for x in input().split()]#inputs an string of numbers, splits it into an array, and then the string is typecasted to an array
if(len(dim) != 2 or dim[0] != dim[1]):#if no. of inputs is not 2 or if the dimensions do not form a square matrix
print("Enter valid dimensions")
else:
break#correct dimensions, so break the loop
print("Enter values for the matrix")
matrix = []
matrix = [int(x) for x in input().split()]#inputs an string of numbers, splits it into an array, and then the string is typecasted to an array
if(len(matrix) != (dim[0] * dim[1])):#invalid no. of numbers
print("Invalid no. of elements for the matrix")
quit()
matrix = np.array(matrix)#converting list into a numpy array
matrix = matrix.reshape(dim[0], dim[1])#reshape numpy array to form an array of specified shape
values, vectors = linalg.eig(matrix)#returns eigen values and eigen vectors
print("Eigen values:")
for value in values:#values is a 1 by n array, value is a complex number
print("%10.3e + %10.3ej"% (value.real, value.imag))#format input as specified
print("Eigen vectors:")
for vector in vectors:#vectors is n by n array
for vect in vector:#vector is a 1 by n array, vect is a complex number
print("%10.3e + %10.3ej"% (vect.real, vect.imag))

Image version of code:

import numpy as np from scipy import linalg dim-[ while (True):#run indefinitely dim-[int (x) for x in input ().split()ㅑinputs an string of numbers, splits it into an array, and then the string is typecasted to an array if (len(dim) !_ 2 or dim[0] !-dim[1]):#if no. of inputs is not 2 or if the dimensions do not form a square matrix print ("Enter valid dimensions") else: break#correct dimensions, s break the loop print("Enter values for the matrix") matrix[ matrix = [int (x) for x în input(). split()) #inputs an string of numbers, splits it into an array, and then the string is typeca sted to an array if (len(matrix) !- (dim [0] * din(1))):#invalid no . of numbers print (Invalid no. of elements for the matrix") quit ) matrix-np.array (matrix) #converting list into a numpy array matrix-matrix. reshape (din [0], dim [1])#reshape numpy array to form an array of specified shape values, vectors-lina1g.eig (matrix) #returns eigen values and eigen vectors print("Eigen values:" for value in values: #values is a 1 by n array print ("%10.3e %10 . Зеј"% (value . real, value . imag)) + print ("Eigen vectors:") for vector in vectors: #ve ctors is n by n array for vect în vector: #vector is a 1 by n array print (" 10 . 3e & 10 . Зеј "% (vect. real, ve ct. imag) ) +

Output:

Enter values for the matrix 10 8 9 7 6 4 3 8 2 Eigen values: 1.951e+01 -7.550e-0 -7, 550е-01 Eigen vectors: 0.000e+00j 2.427e+00 + -2 . 427е+00ј 7.772e-01 0.000e+00j -4.630e-0-3.697e-01 -4.630e-0 3.697e-01 5.113e-0 0.000e+00j -7.384e-02+ 3.566e-01 -7.384е-02 + -3.566е-015 3.668e-0 0.000e+00j 7.186e-01 0.000e+00j 7.186e-01-0.000e+005