Skip to content
Related Articles

Related Articles

Table of Contents

Improve Article
Save Article
Like Article

Check if a given matrix is Hankel or not

  • Last Updated : 26 Apr, 2021

Given a matrix m[][] of size n x n. The task is to check whether given matrix is Hankel Matrix or not.
In linear algebra, a Hankel matrix (or catalecticant matrix), named after Hermann Hankel, is a square matrix in which each ascending skew-diagonal from left to right is constant.
Examples: 

Input: n = 4, 
m[][] = { 
{1, 2, 3, 5}, 
{2, 3, 5, 8}, 
{3, 5, 8, 0}, 
{5, 8, 0, 9} 
}; 
Output: Yes 
All diagonal {1}, {2, 2}, {3, 3, 3}, {5, 5, 5, 5}, {8, 8, 8}, {9} have constant value. 
So given matrix is Hankel Matrix.

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.  To complete your preparation from learning a language to DS Algo and many more,  please refer Complete Interview Preparation Course.

In case you wish to attend live classes with experts, please refer DSA Live Classes for Working Professionals and Competitive Programming Live for Students.

Input: n = 3, 
m[][] = { 
{1, 2, 3}, 
{2, 3, 5}, 
{3, 9, 8} 
}; 
Output: No 



Observe, for a matrix to be Hankel Matrix, it must be of the form, 

a0  a1  a2  a3
a1  a2  a3  a4
a2  a3  a4  a5
a3  a4  a5  a6

Therefore, to check if the given matrix is Hankel Matrix, we need check if each m[i][j] == ai + j. Now, ai + j can be define as: 

         m[i+j][0], if i + j < n
ai + j = 
         m[i + j - n + 1][n-1], otherwise

Below is the implementation of the above approach: 

C++




// C++ Program to check if given matrix is
// Hankel Matrix or not.
#include <bits/stdc++.h>
using namespace std;
#define N 4
 
// Function to check if given matrix is Hankel
// Matrix or not.
bool checkHankelMatrix(int n, int m[N][N])
{
    // for each row
    for (int i = 0; i < n; i++) {
 
        // for each column
        for (int j = 0; j < n; j++) {
 
            // checking if i + j is less than n
            if (i + j < n) {
 
                // checking if the element is equal to the
                // corresponding diagonal constant
                if (m[i][j] != m[i + j][0])
                    return false;
            }
            else {
 
                // checking if the element is equal to the
                // corresponding diagonal constant
                if (m[i][j] != m[i + j - n + 1][n - 1])
                    return false;
            }
        }
    }
 
    return true;
}
 
// Drivers code
int main()
{
    int n = 4;
    int m[N][N] = {
        { 1, 2, 3, 5 },
        { 2, 3, 5, 8 },
        { 3, 5, 8, 0 },
        { 5, 8, 0, 9 }
    };
 
    checkHankelMatrix(n, m) ? (cout << "Yes")
                            : (cout << "No");
    return 0;
}
Java



// Java Program to check if given matrix is
// Hankel Matrix or not.
import java.io.*;
import java.util.*;
 
class GFG {
 
    // Function to check if given matrix
    // is Hankel Matrix or not.
    static boolean checkHankelMatrix(int n,
                                 int m[][])
    {
        // for each row
        for (int i = 0; i < n; i++) {
     
            // for each column
            for (int j = 0; j < n; j++) {
     
                // checking if i + j is less
                // than n
                if (i + j < n) {
     
                    // checking if the element
                    // is equal to the
                    // corresponding diagonal
                    // constant
                    if (m[i][j] != m[i + j][0])
                        return false;
                }
                else {
     
                    // checking if the element
                    // is equal to the
                    // corresponding diagonal
                    // constant
                    if (m[i][j] !=
                       m[i + j - n + 1][n - 1])
                        return false;
                }
            }
        }
     
        return true;
    }
     
    // Drivers code
    public static void main(String args[])
    {
        int n = 4;
        int m[][] = {
            { 1, 2, 3, 5 },
            { 2, 3, 5, 8 },
            { 3, 5, 8, 0 },
            { 5, 8, 0, 9 }
        };
     
        if(checkHankelMatrix(n, m))
            System.out.println("Yes");
        else
            System.out.println("No");
    }
}
 
// This code is contributed by Anuj_67.
Python 3



# Python 3 Program to check if given matrix is
# Hankel Matrix or not.
 
N = 4
 
# Function to check if given matrix is Hankel
# Matrix or not.
def checkHankelMatrix(n, m):
 
    # for each row
    for i in range( 0, n):
 
        # for each column
        for j in range( 0, n):
 
            # checking if i + j is less
            # than n
            if (i + j < n):
 
                # checking if the element is
                # equal to the corresponding
                # diagonal constant
                if (m[i][j] != m[i + j][0]):
                    return False
             
            else :
 
                # checking if the element is
                # equal to the corresponding
                # diagonal constant
                if (m[i][j] !=
                    m[i + j - n + 1][n - 1]):
                    return False
             
    return True
 
# Drivers code
n = 4
m =[[1, 2, 3, 5,],
    [2, 3, 5, 8,],
    [3, 5, 8, 0,],
    [5, 8, 0, 9]]
(print("Yes") if checkHankelMatrix(n, m)
                      else print("No"))
 
# This code is contributed by Smitha.
C#



// C# Program to check if given matrix is
// Hankel Matrix or not.
using System;
 
class GFG {
 
    // Function to check if given matrix
    // is Hankel Matrix or not.
    static bool checkHankelMatrix(int n,
                                int [,]m)
    {
        // for each row
        for (int i = 0; i < n; i++) {
     
            // for each column
            for (int j = 0; j < n; j++) {
     
                // checking if i + j is less
                // than n
                if (i + j < n) {
     
                    // checking if the element
                    // is equal to the
                    // corresponding diagonal
                    // constant
                    if (m[i, j] != m[i + j, 0])
                        return false;
                }
                else {
     
                    // checking if the element
                    // is equal to the
                    // corresponding diagonal
                    // constant
                    if (m[i,j] != m[i + j - n
                                  + 1, n - 1])
                        return false;
                }
            }
        }
     
        return true;
    }
     
    // Drivers code
    public static void Main()
    {
        int n = 4;
        int [,]m = {
            { 1, 2, 3, 5 },
            { 2, 3, 5, 8 },
            { 3, 5, 8, 0 },
            { 5, 8, 0, 9 }
        };
     
        if(checkHankelMatrix(n, m))
            Console.Write("Yes");
        else
            Console.Write("No");
    }
}
 
// This code is contributed by Anuj_67.
PHP



<?php
// PHP Program to check if given matrix is
// Hankel Matrix or not.
$N = 4;
 
// Function to check if
// given matrix is Hankel
// Matrix or not.
function checkHankelMatrix( $n, $m)
{
     
    // for each row
    for($i = 0; $i < $n; $i++) {
 
        // for each column
        for ($j = 0;$j < $n; $j++) {
 
            // checking if i + j
            // is less than n
            if ($i + $j < $n) {
 
                // checking if the element
                // is equal to the corresponding
                // diagonal constant
                if ($m[$i][$j] != $m[$i + $j][0])
                    return false;
            }
            else {
 
                // checking if the element
                // is equal to the
                // corresponding diagonal constant
                if ($m[$i][$j] != $m[$i + $j -
                             $n + 1][$n - 1])
                    return false;
            }
        }
    }
 
    return true;
}
 
    // Driver code
    $n = 4;
    $m = array(array( 1, 2, 3, 5 ),
               array( 2, 3, 5, 8 ),
               array( 3, 5, 8, 0 ),
               array( 5, 8, 0, 9 ));
    if(checkHankelMatrix($n, $m))
        echo "Yes";
    else
        echo "No";
 
// This code is contributed by Anuj_67.
?>
Javascript



<script>
 
// Java script Program to check if given matrix is
// Hankel Matrix or not.
 
 
    // Function to check if given matrix
    // is Hankel Matrix or not.
    function checkHankelMatrix(n,m)
    {
        // for each row
        for (let i = 0; i < n; i++) {
     
            // for each column
            for (let j = 0; j < n; j++) {
     
                // checking if i + j is less
                // than n
                if (i + j < n) {
     
                    // checking if the element
                    // is equal to the
                    // corresponding diagonal
                    // constant
                    if (m[i][j] != m[i + j][0])
                        return false;
                }
                else {
     
                    // checking if the element
                    // is equal to the
                    // corresponding diagonal
                    // constant
                    if (m[i][j] !=
                    m[i + j - n + 1][n - 1])
                        return false;
                }
            }
        }
     
        return true;
    }
     
    // Drivers code
     
        let n = 4;
        let m = [
            [1, 2, 3, 5 ],
            [ 2, 3, 5, 8] ,
            [ 3, 5, 8, 0 ],
            [ 5, 8, 0, 9 ]
        ];
     
        if(checkHankelMatrix(n, m))
            document.write("Yes");
        else
            document.write("No");
 
//this code is  contributed by mohan pavan pulamolu
</script>
Output
Yes
Time Complexity: O(N2)
Auxiliary Space: O(1)



My Personal Notes
arrow_drop_up
Previous
AWS EC2 Instance Setup with Apache Server
Next

Java Swing | JSlider
Recommended Articles
Page :
Check if it is possible to make the given matrix increasing matrix or not
30, May 18
Program to check if a matrix is Binary matrix or not
04, Oct 18
Check if a given matrix can be converted to another given matrix by row and column exchanges
30, Apr 20
Generate a Matrix such that given Matrix elements are equal to Bitwise OR of all corresponding row and column elements of generated Matrix
15, Jan 21
Generate matrix from given Sparse Matrix using Linked List and reconstruct the Sparse Matrix
19, Apr 21
Check if a given matrix is sparse or not
08, Oct 17
Check whether a given matrix is orthogonal or not
21, Feb 18
Check given matrix is magic square or not
27, Feb 18
Check if the Matrix follows the given constraints or not
28, Jun 20
Check whether the given Matrix is balanced or not
06, Aug 20
Check if a path exists from a given cell to any boundary element of the Matrix with sum of elements not exceeding K
31, Mar 21
Check if there are T number of continuous of blocks of 0s or not in given Binary Matrix
07, Oct 21
C Program To Check whether Matrix is Skew Symmetric or not
06, Mar 17
Program to check if matrix is singular or not
25, Feb 18
Check whether a Matrix is a Latin Square or not
19, Apr 20
Check if row-major order path of Matrix is palindrome or not
20, Jun 20
Check if Matrix sum is prime or not
26, Jun 20
Check if a Matrix is Bitonic or not
18, Jul 20
Check if a Matrix is Reverse Bitonic or Not
25, Jul 20
Check if all rows of a Binary Matrix have all ones placed adjacently or not
23, Feb 21
Check if all the diagonals of the Matrix are palindromic or not
07, Oct 21
Check if diagonal elements of a Matrix are Prime or not
16, Feb 21
Check if two elements of a matrix are on the same diagonal or not
12, Sep 20
Program to check diagonal matrix and scalar matrix
10, Jan 18
Article Contributed By :
https://media.geeksforgeeks.org/auth/avatar.png
anuj0503
@anuj0503
Vote for difficulty





Improved By :
Article Tags :
Practice Tags :
Report Issue

We use cookies to ensure you have the best browsing experience on our website. By using our site, you
acknowledge that you have read and understood our
Cookie Policy &
        Privacy Policy

Lightbox

Start Your Coding Journey Now!