identity_matrix_recognizer.py

# from cs 101 course of udacity.com (problem set solved solution)

# Given a list of lists representing a n * n matrix as input, 
# define a  procedure that returns True if the input is an identity matrix 
# and False otherwise.

# An IDENTITY matrix is a square matrix in which all the elements 
# on the principal/main diagonal are 1 and all the elements outside 
# the principal diagonal are 0. 
# (A square matrix is a matrix in which the number of rows 
# is equal to the number of columns)

def is_identity_matrix(matrix):
    total_elems = 0
    last_pos = 0
    for row in matrix:
        total_elems += len(row)
        if row[last_pos] == 1 and row.count(0) == len(row) - 1:
            last_pos += 1
        else:
            return False
    if total_elems == len(matrix[0]) * len(matrix[0]):
        return True
    else:
        return False


# Test Cases:

matrix1 = [[1,0,0,0],
           [0,1,0,0],
           [0,0,1,0],
           [0,0,0,1]]
print is_identity_matrix(matrix1)
#>>>True

matrix2 = [[1,0,0],
           [0,1,0],
           [0,0,0]]

print is_identity_matrix(matrix2)
#>>>False

matrix3 = [[2,0,0],
           [0,2,0],
           [0,0,2]]

print is_identity_matrix(matrix3)
#>>>False

matrix4 = [[1,0,0,0],
           [0,1,1,0],
           [0,0,0,1]]

print is_identity_matrix(matrix4)
#>>>False

matrix5 = [[1,0,0,0,0,0,0,0,0]]

print is_identity_matrix(matrix5)
#>>>False

matrix6 = [[1,0,0,0],  
           [0,1,0,1],  
           [0,0,1,0],  
           [0,0,0,1]]

print is_identity_matrix(matrix6)
#>>>False

matrix7 = [[1, -1, 1],
           [0, 1, 0],
           [0, 0, 1]]
print is_identity_matrix(matrix7)
#>>>False