Check if the matrix is lower triangular using Python

In this article, we will learn a python program to check if a matrix is lower triangular.

Assume we have taken an input matrix. We will now check whether the input matrix is lower triangular using the below methods.

Methos Used

The following are the various methods to accomplish this task −

• Using nested for loop

What is a Lower Triangular Matrix?

If all the entries above the main/principal diagonal are zero, a square matrix is said to be lower triangular.

Example

1 0 0 0 
2 3 0 0 
1 3 7 0 
0 4 8 4 

Method 1: Using Nested for Loop

Algorithm (Steps)

Following are the Algorithms/steps to be followed to perform the desired task. −

• Create a function printGivenMatrix() that prints the given matrix.

• Inside the printGivenMatrix() function Traverse through the rows of the given Matrix using For loop.

• Using another Nested For loop traverse through the columns of the current row.

• Print the corresponding matrix element at the current row and column.

• Create a function checkLowerTriangular() to check whether the input matrix is lower triangular by accepting the input matrix as an argument.

• Use the for loop to traverse through the length of rows of a matrix using the len() function(returns the number of items in an object).

• Use another nested for loop to traverse through the from (row +1) column to the end of the columns.

• Use the if conditional statement to check whether the current element is not equal to 0(So the lower triangular Condition Fails)

• Return False if the condition is true using the return statement.

• If all the nested loops get executed without returning anything then the given matrix is lower triangular so return True.

• Create a variable to store the input matrix.

• Print the given matrix by passing this as an argument to printGivenMatrix()

• Use the if conditional statement to check whether the above-defined function checkLowerTriangular() function returns true by passing the input matrix as an argument.

• Print the input matrix as a lower triangular matrix if the condition is true.

• Else print the input matrix is NOT a lower triangular matrix.

Example

The following program returns whether the given matrix is lower triangular or not using nested For loops −

# creating a function to print the given matrix
def printGivenMatrix(inputMatrix):
   # Traversing in the rows of the input matrix
      for p in range(len(inputMatrix)):
         # Traversing in the columns corresponding to the current row
         # of the input matrix
            for q in range(len(inputMatrix)):
               # printing the element at the current row and column
                  print(inputMatrix[p][q], end=" ")
            # Printing a new line to separate the rows
            print()
# createing a function to check whether the matrix
# is lower triangular by accepting the input matrix as an argument
def checkLowerTriangular(inputMatrix):
   # traversing through the rows of a matrix
      for p in range(0, len(inputMatrix)):
         # Traversing from row +1 column to last column
         for q in range(p + 1, len(inputMatrix)):
            # checking whether the current element is not equal to 0
               if(inputMatrix[p][q] != 0):
                  # If the element is not zero then it cannot be considered as lower triangular
                  # Hence returning false if the condition is true
                     return False
   # If the above nested loops get executed without returning False
   # Hence the matrix is lower triangular so return True
      return True
# input matrix
inputMatrix = [[1, 0, 0, 0],
               [2, 3, 0, 0],
               [1, 3, 7, 0],
               [0, 4, 8, 4]]
# Printing the given input Matrix by passing the
# given matrix as an argument to printGivenMatrix() function
printGivenMatrix(inputMatrix)
# checking whether the checkLowerTriangular() returns true
if checkLowerTriangular(inputMatrix):
   # If the function returns True then the matrix is lower triangular
      print("Yes, the input matrix is lower triangular!!!")
else:
   # else printing NOT lower triangular matrix
      print("No, the input matrix is Not lower triangular!!!")

Output

On executing, the above program will generate the following output −

1 0 0 0 
2 3 0 0 
1 3 7 0 
0 4 8 4 
Yes, the input matrix is lower triangular!!!

Time Complexity − O(n^2). In which n indicates the number of rows and columns in the specified matrix.

Auxiliary Space − O(1). as no extra space is required, hence it is a constant.

Conclusion

We learned what a lower triangular matrix is in this article along with an example, and at the end, we wrote code with instructions on how to determine whether a given matrix is a lower triangular matrix or not.