# Python Program to check whether given matrix is a Hankel matrix or not

In this article, we will learn how to check whether a given matrix is a Hankel matrix or not.

The Hankel matrix is a square matrix in which each ascending skew-diagonal from left to right is constant. The Hankel matrix is a symmetric matrix. To know more about the Hankel matrix click here

Example

```Input: matrix = [[1, 2, 3, 5],
[2, 3, 5, 8],
[3, 5, 8, 0],
[5, 8, 0, 9]]
Output: Hankel matrix```

## Hankel Matrix in Python

1. Load the input matrix.

2. Iterate through every row and column of the matrix.

3. Now check, whether the current element is equal to the corresponding diagonal constant if not return false

4. Else, return true.

```def Hankelmatrix(matrix):
n = len(matrix)
# for each row
for i in range(n):
# for each column
for j in range(n):
if (i+j<n):
if (matrix[i][j]!=matrix[i+j]):
return False
else:
if (matrix[i][j] != matrix[i+j-n+1][n-1]):
return False
return True
matrix = [[1, 4, 3, 5],
[4, 3, 5, 6],
[3, 5, 6, 0],
[5, 6, 0, 1]]
print("The given matrix: ")
for i in range(len(matrix)):
for j in range(len(matrix)):
print(matrix[i][j], end= ' ')
print()
if(Hankelmatrix(matrix)):
print("Hankel matrix")
else:
print("Not a Hankel matrix")```

Output

```The given matrix:
1 4 3 5
4 3 5 6
3 5 6 0
5 6 0 1
Hankel matrix

The given matrix:
1 14 3 5
4 6 5 61
3 5 6 10
5 6 0 8
Not a Hankel matrix```

Also, refer: