4.7. Is Diagonal

In mathematics, a diagonal matrix is a matrix in which all non-diagonal entries are zero. That is, \(\mathbf{A_{i,j} = 0}\) if \(\mathbf{i\neq j}\). Since it is easier to work with diagonal matrices, we should check them if they are diagonal or not.

Write a function called is_diagonal that takes an \(\mathbf{n\times n}\) matrix as a list of list of integers and returns a Boolean value stating whether the matrix is diagonal or not.

Note that in a diagonal matrix, diagonal entries can be zero as well, but in our case diagonal entries are non-zero integers.

Hint: There is a list method that returns the number of occurrences of a given element in that list.

Sample I/O:

>>> is_diagonal([[1,0,0],[0,1,0],[0,0,1]])
True

>>> is_diagonal([[1,1,1],[2,4,0],[3,3,3]])
False

Show the Answer

def is_diagonal(matrix):
    n = len(matrix)

    for i in range(n):
        zeros = matrix[i].count(0)
        if(zeros != n-1 or matrix[i][i] == 0):
            return False

    return True